A182845 -id:A182845

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A182844

a(0)=0: a(n)=A002865(2*n)+A002865(2*n+1), n>=1.

+10
3

0, 2, 4, 8, 15, 26, 45, 75, 121, 193, 302, 463, 703, 1052, 1555, 2277, 3301, 4740, 6754, 9548, 13398, 18678, 25873, 35620, 48771, 66418, 89988, 121345, 162878, 217666, 289685, 383994, 507059, 667131, 874656, 1142860, 1488484, 1932575, 2501599, 3228787

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

a(n) is also the length of the n-th "large mirror" of the "mirror" version of the shell model of partitions A135010.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..1000

EXAMPLE

a(0)=0 by definition. a(1)=1+1=2: a(2)=2+2=4. a(3)=4+4=8. a(4)=7+8=15. a(5)=12+14=26. a(6)=21+24=45.

CROSSREFS

Cf. A002865, A135010. For another version see A182845.

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Jan 24 2011

EXTENSIONS

Extended by Nathaniel Johnston, May 06 2011

STATUS

approved

A374921

Irregular triangle read by rows: T(n,k), n >= 0, k >= 1, in which if n is even then row n lists the first A008619(n) even indexed terms of A027336 otherwise if n is odd then row n lists the first A008619(n) odd indexed terms of A027336.

+10
0

1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 4, 1, 1, 3, 6, 1, 2, 4, 8, 1, 1, 3, 6, 11, 1, 2, 4, 8, 15, 1, 1, 3, 6, 11, 20, 1, 2, 4, 8, 15, 26, 1, 1, 3, 6, 11, 20, 35, 1, 2, 4, 8, 15, 26, 45, 1, 1, 3, 6, 11, 20, 35, 58, 1, 2, 4, 8, 15, 26, 45, 75, 1, 1, 3, 6, 11, 20, 35, 58, 96, 1, 2, 4, 8, 15, 26, 45, 75, 121

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

COMMENTS

The sum of row n equals the number of partitions of n.

LINKS

Table of n, a(n) for n=0..89.

EXAMPLE

Triangle begins:

1, 1;

1, 2;

1, 1, 3;

1, 2, 4;

1, 1, 3, 6;

1, 2, 4, 8;

1, 1, 3, 6, 11;

1, 2, 4, 8, 15;

1, 1, 3, 6, 11, 20;

1, 2, 4, 8, 15, 26;

1, 1, 3, 6, 11, 20, 35;

1, 2, 4, 8, 15, 26, 45;

1, 1, 3, 6, 11, 20, 35, 58;

1, 2, 4, 8, 15, 26, 45, 75;

1, 1, 3, 6, 11, 20, 35, 58, 96;

1, 2, 4, 8, 15, 26, 45, 75, 121;

...

For n = 10 the sum of the 10th row is 1 + 1 + 3 + 6 + 11 + 20 = 42, the same as the number of partitions of 10.

CROSSREFS

Row sums give A000041.

Row lengths give A008619.

Right border gives A027336.

Columns 1..4: A000012, A000034, A010702, A010724.

Cf. A058695, A058696, A002865, A167430, A176206, A182844, A182845, A336811, A338156.

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Aug 01 2024

STATUS

approved

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