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

0,2

Comments

Row sums are A134931(n).

Diagonal sums are A140253(n).

Compare this sequence with A207627.

Column k is divisible by 2^k.

Links

Table of n, a(n) for n=0..53.

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).

Example

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

Sequence in context: A226367 A324934 A240271 * A277416 A064691 A247071

Adjacent sequences: A208321 A208322 A208323 * A208325 A208326 A208327

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Feb 25 2012

Status

approved