A208324 Triangle T(n,k), read by rows, given by (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (4, -2, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 2, 4, 3, 10, 8, 4, 18, 28, 16, 5, 28, 64, 72, 32, 6, 40, 120, 200, 176, 64, 7, 54, 200, 440, 576, 416, 128, 8, 70, 308, 840, 1456, 1568, 960, 256, 9, 88, 448, 1456, 3136, 4480, 4096, 2176, 512, 10, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864

Offset: 0

Author

Philippe Deléham, Feb 25 2012

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A134931(n).

Diagonal sums are A140253(n).

Compare this sequence with A207627.

Column k is divisible by 2^k.

Examples

			Triangle begins :
1
2, 4
3, 10, 8
4, 18, 28, 16
5, 28, 64, 72, 32
6, 40, 120, 200, 176, 64
7, 54, 200, 440, 576, 416, 128
8, 70, 308, 840, 1456, 1568, 960, 256
9, 88, 448, 1456, 3136, 4480, 4096, 2176, 512
10, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864, 1024
		

Crossrefs

Cf. A207627

Formula

T(n,0) = n+1.

T(n,1) = 2*T(n,0) + T(n-1,1).

T(n,k) = 2*T(n-1,k-1) + T(n-1,k) for k>1.

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1) with T(0,0) = 1, T(1,0) = 2, T(1,1) = 4.

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