A210239 Triangle, read by rows, given by (2, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 2, 2, 2, 5, 3, 2, 9, 12, 5, 2, 13, 28, 25, 8, 2, 17, 52, 74, 50, 13, 2, 21, 84, 167, 177, 96, 21, 2, 25, 124, 320, 470, 397, 180, 34, 2, 29, 172, 549, 1041, 1211, 850, 331, 55, 2, 33, 228, 870, 2034, 3042, 2928, 1758, 600, 89

Offset

0,2

Links

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

Formula

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

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

Sum_{k, 0<=k<=n} T(n,k)*x^k = A122803(n), A000007(n), A040000(n), A026150(n+1) for x = -2, -1, 0, 1 respectively.

T(n,n) = Fibonacci(n+2) = A000045(n+2), T(n+1,n) = A067331(n).

Example

Triangle begins :
1
2, 2
2, 5, 3
2, 9, 12, 5
2, 13, 28, 25, 8
2, 17, 52, 74, 50, 13
2, 21, 84, 167, 177, 96, 21
2, 25, 124, 320, 470, 397, 180, 34

Crossrefs

Cf. A000045, A026150, A112087 (3rd column, n>2).

Sequence in context: A228917 A061311 A174960 * A115253 A154429 A333388

Adjacent sequences: A210236 A210237 A210238 * A210240 A210241 A210242

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Mar 19 2012

Status

approved