The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Reinhard Zumkeller (See also Reinhard Zumkeller's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A265848

Pascal's triangle, right and left halves interchanged.
(history; published version)

#15 by Reinhard Zumkeller at Fri Dec 25 12:14:44 EST 2015

STATUS

editing

approved

#14 by Reinhard Zumkeller at Fri Dec 25 11:29:01 EST 2015

COMMENTS

T(n,k) = if k <= [(n+1)/2] then A014413(n,k+1) for else A034868(n > 0 and ,k = 0 .. floor(-[(n+1)/2]);

FORMULA

T(n,k) = A007318(n, (k + floor((n+2)/2)) mod (n+1)).

A014413

Triangular array formed from elements to right of middle of Pascal's triangle.
(history; published version)

#11 by Reinhard Zumkeller at Fri Dec 25 03:52:14 EST 2015

LINKS

Reinhard Zumkeller, <a href="/A014413/b014413.txt">Rows n = 01..200 of triangle, flattened</a>

Discussion

Sat Feb 13

10:31

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A014413 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#10 by Reinhard Zumkeller at Fri Dec 25 03:49:51 EST 2015

EXAMPLE

1;

3, 1;

4, 1;

10, 5, 1;

15, 6, 1;

35, 21, 7, 1;

56, 28, 8, 1;

126, 84, 36, 9, 1;

210, 120, 45, 10, 1;

462, 330, 165, 55, 11, 1;

792, 495, 220, 66, 12, 1.

A014462

Triangular array formed from elements to left of middle of Pascal's triangle.
(history; published version)

#16 by Reinhard Zumkeller at Fri Dec 25 03:42:06 EST 2015

LINKS

Reinhard Zumkeller, <a href="/A014462/b014462.txt">Rows n = 01..200 of triangle, flattened</a>

PROG

a014462 n k = a014462_tabf !! (n -1) !! (k-1)

a014462_row n = a014462_tabf !! (n-1)

Discussion

Sat Feb 13

10:31

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A014462 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

A265848

Pascal's triangle, right and left halves interchanged.
(history; published version)

#13 by Reinhard Zumkeller at Thu Dec 24 00:49:57 EST 2015

COMMENTS

Concatenations of rows of A014413 and A034868;

T(n,k) = A014413(k+1) for n > 0 and k = 0 .. floor((n+1)/2);

alternative mirrored variant: concatenation of A034869 and A014462;

T(n,0) = A037952(n) for n > 0;

T(n,n) = A001405(n).

LINKS

Reinhard Zumkeller, <a href="/A265848/b265848.txt">Table of n, a(n) for Rows n = 0..11475150 of triangle, flattened</a>

<a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

EXAMPLE

. 0: 1

. 1: 1 1

. 2: 1 1 2

. 3: 3 1 1 3

. 4: 4 1 1 4 6

. 5: 10 5 1 1 5 10

. 6: 15 6 1 1 6 15 20

. 7: 35 21 7 1 1 7 21 35

. 8: 56 28 8 1 1 8 28 56 70

. 9: 126 84 36 9 1 1 9 36 84 126

. 10: 210 120 45 10 1 1 10 45 120 210 252

. 11: 462 330 165 55 11 1 1 11 55 165 330 462

. 12: 792 495 220 66 12 1 1 12 66 220 495 792 924 .

PROG

(Haskell)

a265848 n k = a265848_tabl !! n !! k

a265848_row n = a265848_tabl !! n

a265848_tabl = zipWith (++) ([] : a014413_tabf) a034868_tabf

CROSSREFS

Cf. A014413, A014462, A034868, A034869, A007318, A001405, A037952, A000079 (row sums), A001142 (row products).

KEYWORD

nonn,changed,tabl

#12 by Reinhard Zumkeller at Thu Dec 24 00:46:33 EST 2015

NAME

allocated for Reinhard ZumkellerPascal's triangle, right and left halves interchanged.

DATA

1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 4, 1, 1, 4, 6, 10, 5, 1, 1, 5, 10, 15, 6, 1, 1, 6, 15, 20, 35, 21, 7, 1, 1, 7, 21, 35, 56, 28, 8, 1, 1, 8, 28, 56, 70, 126, 84, 36, 9, 1, 1, 9, 36, 84, 126, 210, 120, 45, 10, 1, 1, 10, 45, 120, 210, 252, 462, 330, 165, 55, 11, 1, 1, 11, 55, 165, 330, 462

OFFSET

0,6

LINKS

Reinhard Zumkeller, <a href="/A265848/b265848.txt">Table of n, a(n) for n = 0..11475</a>

KEYWORD

allocated

nonn

AUTHOR

Reinhard Zumkeller, Dec 24 2015

STATUS

approved

editing

A034869

Right half of Pascal's triangle.
(history; published version)

#18 by Reinhard Zumkeller at Thu Dec 24 00:44:03 EST 2015

CROSSREFS

Cf. A034868 (left half), A014413, A014462.

STATUS

approved

editing

Discussion

Fri Feb 12

07:48

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A034869 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

A034868

Left half of Pascal's triangle.
(history; published version)

#29 by Reinhard Zumkeller at Thu Dec 24 00:40:45 EST 2015

CROSSREFS

Cf. A034869 (right half), A014413, A014462, A265848.

STATUS

approved

editing

Discussion

Fri Feb 12

07:48

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A034868 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

A014462

Triangular array formed from elements to left of middle of Pascal's triangle.
(history; published version)

#15 by Reinhard Zumkeller at Thu Dec 24 00:39:04 EST 2015

LINKS

Reinhard Zumkeller, <a href="/A014462/b014462.txt">Table Rows n = 0..200 of n, a(n) for n = 1..10201triangle, flattened</a>

PROG

(Haskell)

a014462 n k = a014462_tabf !! n !! k

a014462_row n = a014462_tabf !! n

a014462_tabf = map reverse a014413_tabf

-- Reinhard Zumkeller, Dec 24 2015

CROSSREFS

Cf. A007318.