A182436 Triangle T(n,k), read by rows, given by (2, -1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 2, 1, 2, 5, 2, 4, 8, 11, 4, 4, 20, 25, 24, 8, 8, 28, 70, 69, 52, 16, 8, 60, 126, 213, 178, 112, 32, 16, 80, 288, 460, 599, 440, 240, 64, 16, 160, 472, 1128, 1489, 1600, 1056, 512, 128, 32, 208, 976, 2152, 3914, 4457, 4120, 2480, 1088, 256

Offset: 0

Author

Philippe Deléham, Apr 28 2012

Keywords

• easy
• nonn
• tabl

Comments

Row sums are the powers of 3.

Examples

			Triangle begins :
1
2, 1
2, 5, 2
4, 8, 11, 4
4, 20, 25, 24, 8
8, 28, 70, 69, 52, 16
8, 60, 126, 213, 178, 112, 32
16, 80, 288, 460, 599, 440, 240, 64
16, 160, 472, 1128, 1489, 1600, 1056, 512, 128
32, 208, 976, 2152, 3914, 4457, 4120, 2480, 1088, 256
		

Crossrefs

Cf. A016116, A011782, A111297, A000244

Formula

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

T(n,k) = 2*T(n-1,k-1) + 2*T(n-2,k) + T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = T(2,0) = T(2,2) = 2, T(2,1) = 5 and T(n,k) = 0 if k<0 or if k>n.

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A123335(n-1), A016116(n+1), A000244(n), A057087(n), A091928(n) for x = -2, -1, 0, 1, 2, 3 respectively.