A210637 Triangle T(n,k), read by rows, given by (2, 1/2, -1/2, 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, 5, 8, 3, 12, 27, 20, 5, 29, 84, 91, 44, 8, 70, 248, 352, 251, 90, 13, 169, 708, 1240, 1164, 618, 176, 21, 408, 1973, 4106, 4771, 3344, 1414, 334, 34, 985, 5400, 13010, 18000, 15645, 8748, 3073, 620, 55

Offset

0,2

Comments

Row sums are powers of 4 (A000302).

Links

Table of n, a(n) for n=0..44.

Formula

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

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k) + 2*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 = (-1)^n*A159612(n+1), (-1)^n*A000034(n), A000007(n), A000129(n+1), A000302(n) for x = -3, -2, -1, 0, 1 respectively.

T(n,0) = A000129(n+1), T(n,n) = A000045(n+2), T(n+1,n) = 2*A004798(n+1).

Example

Triangle begins :
1
2, 2
5, 8, 3
12, 27, 20, 5
29, 84, 91, 44, 8
70, 248, 352, 251, 90, 13
169, 708, 1240, 1164, 618, 176, 21
408, 1973, 4106, 4771, 3344, 1414, 334, 34
985, 5400, 13010, 18000, 15645, 8748, 3073, 620, 55
2378, 14574, 39880, 63966, 66282, 46014, 21400, 6429, 1132, 89
5741, 38896, 119129, 217232, 261185, 216348, 125028, 49772, 13061, 2040, 144

Crossrefs

Cf. A000045, A000129, A000302, A261056 (2nd column).

Sequence in context: A193891 A193906 A224791 * A201972 A202396 A210804

Adjacent sequences: A210634 A210635 A210636 * A210638 A210639 A210640

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Mar 26 2012

Status

approved