A210636 Riordan array ((1-x)/(1-2*x-x^2), x*(1+x)/(1-2*x-x^2)).

1, 1, 1, 3, 4, 1, 7, 13, 7, 1, 17, 40, 32, 10, 1, 41, 117, 124, 60, 13, 1, 99, 332, 437, 286, 97, 16, 1, 239, 921, 1447, 1193, 553, 143, 19, 1, 577, 2512, 4584, 4556, 2682, 952, 198, 22, 1, 1393, 6761, 14048, 16336, 11666, 5282, 1510, 262, 25, 1

Offset

0,4

Comments

Triangle T(n,k), 0<=k<=n, read by rows, given by (1, 2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Product of A122542 and A007318 (Pascal's triangle) as lower triangular matrices .

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1), T(0,0) = T(1,0) = T(1,1) = 1 and T(n,k) = 0 if k<0 or if k>n.

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

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A001333(n), A104934(n), A122958(n), A122690(n), A091928(n) for x = -1, 0, 1, 2, 3, 4 respectively.

Example

Triangle begins :
1
1, 1
3, 4, 1
7, 13, 7, 1
17, 40, 32, 10, 1
41, 117, 124, 60, 13, 1
99, 332, 437, 286, 97, 16, 1
239, 921, 1447, 1193, 553, 143, 19, 1
577, 2512, 4584, 4556, 2682, 952, 198, 22, 1
1393, 6761, 14048, 16336, 11666, 5282, 1510, 262, 25, 1

Crossrefs

Cf. Columns :A001333, A119915, Diagonals : A000012, A016777, Antidiagonal sums : A077995

Sequence in context: A053707 A075052 A111516 * A116392 A324559 A174607

Adjacent sequences: A210633 A210634 A210635 * A210637 A210638 A210639

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Mar 26 2012

Status

approved