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Search: a162522 -id:a162522
Displaying 1-8 of 8 results found.
page 1
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A162521
Magic numbers A018226 divided by 2.
+10
7
1, 4, 10, 14, 25, 41, 63
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Sequence related to atomic nuclei.
LINKS
Table of n, a(n) for n=1..7.
CROSSREFS
Cf. A018226, A130517, A130556, A130598, A130602, A162522, A162523, A162524, A162525.
KEYWORD
fini,full,nonn
AUTHOR
Omar E. Pol, Jul 06 2009
STATUS
approved
A162523
First differences of magic numbers A018226, divided by 2.
+10
7
3, 6, 4, 11, 16, 22
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Sequence related to atomic nucleus.
LINKS
Table of n, a(n) for n=1..6.
FORMULA
a(n) = A162522(n)/2.
CROSSREFS
Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162524, A162525.
KEYWORD
fini,full,nonn
AUTHOR
Omar E. Pol, Jul 06 2009
STATUS
approved
A162524
Partial sums of magic numbers A018226.
+10
7
2, 10, 30, 58, 108, 190, 316
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Sequence related to atomic nuclei.
LINKS
Table of n, a(n) for n=1..7.
CROSSREFS
Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162523, A162525.
KEYWORD
fini,full,nonn
AUTHOR
Omar E. Pol, Jul 06 2009
EXTENSIONS
Edited by Omar E. Pol, Jul 16 2009
STATUS
approved
A162525
Partial sums of magic numbers A018226, divided by 2.
+10
7
1, 5, 15, 29, 54, 95, 158
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Sequence related to atomic nuclei.
LINKS
Table of n, a(n) for n=1..7.
FORMULA
a(n) = A162524(n)/2.
CROSSREFS
Cf. A018226, A130517, A130556, A130598, A130602, A162521, A162522, A162523, A162524.
KEYWORD
fini,full,nonn
AUTHOR
Omar E. Pol, Jul 06 2009
STATUS
approved
A162518
Characteristic function of magic numbers A018226: 1 if n is a magic number else 0.
+10
3
0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Sequence related to atomic nuclei.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for characteristic functions
PROG
(PARI) A162518(n) = if(n<1, 0, polcoeff( x^126+x^82+x^50+x^28+x^20+x^8+x^2, n)); \\ Antti Karttunen, Dec 24 2018, after code in A089011
CROSSREFS
Cf. A018226, A130517, A130556, A130598, A130602, A162519, A162521, A162522, A162523, A162524, A162525.
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jul 07 2009
EXTENSIONS
Data section extended up to a(126) by Antti Karttunen, Dec 24 2018
STATUS
approved
A162626
If 0 <= n <= 3 then a(n) = n(n+1)(n+2)/3, if n >= 4 then a(n) = n(n^2+5)/3.
+10
3
0, 2, 8, 20, 28, 50, 82, 126, 184, 258, 350, 462, 596, 754, 938, 1150, 1392, 1666, 1974, 2318, 2700, 3122, 3586, 4094, 4648, 5250, 5902, 6606, 7364, 8178, 9050, 9982, 10976, 12034, 13158, 14350, 15612, 16946, 18354, 19838, 21400, 23042, 24766, 26574
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
One way to generalize the magic number sequence in A018226.
See also A130598 and A162630.
LINKS
Table of n, a(n) for n=0..43.
FORMULA
From Daniel Forgues, May 03 2011: (Start)
If 0 <= n <= 3 then a(n) = 2 T_n, otherwise a(n) = 2 (T_n - t_{n-1}), where T_n is the n-th tetrahedral number, t_n the n-th triangular number.
G.f.: (2*x*(1 - 6*x^3 + 14*x^4 - 11*x^5 + 3*x^6))/(1 - x)^4, n >= 0.
(End)
a(n) = n*(n^2+5)/3 + (4*n-6)*A171386(n). - Omar E. Pol, Aug 14 2013
CROSSREFS
Cf. A007290, A018226, A033547, A130598, A162518, A162519, A162521, A162522, A162523, A162524, A162525, A162630.
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Jul 07 2009, Jul 13 2009
EXTENSIONS
Edited by N. J. A. Sloane, Jul 18 2009
STATUS
approved
A162519
Characteristic function of magic numbers A018226: 0 if n is a magic number else 1.
+10
2
1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also, successive digits of A130598.
This sequence is related to atomic nuclei. See also A162518.
LINKS
Table of n, a(n) for n=1..105.
Index entries for characteristic functions
CROSSREFS
Cf. A018226, A130517, A130556, A130598, A130602, A162518, A162521, A162522, A162523, A162524, A162525.
KEYWORD
fini,nonn
AUTHOR
Omar E. Pol, Jul 07 2009
STATUS
approved
A210842
Number of states in the n-th shell of the nuclear shell model.
+10
2
2, 6, 12, 8, 22, 32, 44, 58
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Partial sums of the first seven terms give the "magic numbers" A018226.
Also the partial sums of the first eight terms give the positive first eight terms of A162626 (and possibly more).
REFERENCES
M. Goeppert Mayer and J. Hans D. Jensen, Elementary Theory of Nuclear Shell Structure, J. Wiley and Sons, Inc. (1955).
I. Talmi, Simple Models of Complex Nuclei, Hardwood Academic Publishers (1993).
LINKS
Table of n, a(n) for n=1..8.
CROSSREFS
Row sums of triangle A212122.
Cf. A018226, A130517, A162522, A162626, A162630, A212121, A212123, A212124, A213361-A213364.
KEYWORD
nonn,hard,more
AUTHOR
Omar E. Pol, Jun 04 2012
STATUS
approved
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