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A091533 Triangle read by rows, related to Pascal's triangle. 5
1, 1, 1, 2, 3, 2, 3, 7, 7, 3, 5, 15, 21, 15, 5, 8, 30, 53, 53, 30, 8, 13, 58, 124, 157, 124, 58, 13, 21, 109, 273, 417, 417, 273, 109, 21, 34, 201, 577, 1029, 1239, 1029, 577, 201, 34, 55, 365, 1181, 2405, 3375, 3375, 2405, 1181, 365, 55, 89, 655, 2358, 5393, 8625, 10047, 8625, 5393, 2358, 655, 89, 144, 1164, 4614, 11702, 20979, 27827, 27827, 20979, 11702, 4614, 1164, 144, 233, 2052, 8880, 24722, 49057, 72871, 82951, 72871, 49057, 24722, 8880, 2052, 233 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Seiichi Manyama, Rows n = 0..139, flattened

FORMULA

T(n, k) = T(n-1, k) + T(n-1, k-1) + T(n-2, k) + T(n-2, k-1) + T(n-2, k-2) for n >= 2, k >= 0, with initial conditions specified by first two rows.

G.f.: A(x, y) = 1/(1-x-x*y-x^2-x^2*y-x^2*y^2).

Sum_{k = 0..n} T(n,k)*x^k = A000045(n+1), A015518(n+1), A015524(n+1), A200069(n+1) for x = 0, 1, 2, 3 respectively. - Philippe Deléham, Oct 30 2013

Sum_{k = 0..floor(n/2)} T(n-k,k) = (-1)^n*A079926(n). - Philippe Deléham, Oct 30 2013

EXAMPLE

This triangle begins

1;

1, 1;

2, 3, 2;

3, 7, 7, 3;

5, 15, 21, 15, 5;

8, 30, 53, 53, 30, 8;

13, 58, 124, 157, 124, 58, 13;

21, 109, 273, 417, 417, 273, 109, 21;

34, 201, 577, 1029, 1239, 1029, 577, 201, 34;

55, 365, 1181, 2405, 3375, 3375, 2405, 1181, 365, 55;

89, 655, 2358, 5393, 8625, 10047, 8625, 5393, 2358, 655, 89;

144, 1164, 4614, 11702, 20979, 27827, 27827, 20979, 11702, 4614, 1164, 144;

233, 2052, 8880, 24722, 49057, 72871, 82951, 72871, 49057, 24722, 8880, 2052, 233; ...

CROSSREFS

Row sums: A015518(n+1). Columns 0-1: A000045(n+1), A023610(n-1).

Cf. A090174, A212338 (column 2), A192364 (central terms).

Sequence in context: A085204 A228527 A055375 * A055376 A085215 A076731

Adjacent sequences:  A091530 A091531 A091532 * A091534 A091535 A091536

KEYWORD

nonn,easy,tabl

AUTHOR

Christian G. Bower, Jan 19 2004

STATUS

approved

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Last modified March 20 09:50 EDT 2019. Contains 321345 sequences. (Running on oeis4.)