A182059 Triangle, read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (2, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 0, 2, 0, 4, 4, 0, 6, 12, 8, 0, 8, 24, 32, 16, 0, 10, 40, 80, 80, 32, 0, 12, 60, 160, 240, 192, 64, 0, 14, 84, 280, 560, 672, 448, 128, 0, 16, 112, 448, 1120, 1792, 1792, 1024, 256, 0, 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512

Offset

0,3

Comments

Row sums are 3^n - 1 + 0^n.

Triangle of coefficients in expansion of (1+2*x)^n - 1 + 0^n .

Links

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

Formula

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

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1), T(0,0) = 1, T(1,0) = T(2,0) = 0, T(1,1) = 2, T(2,1) = T(2,2) = 4 and T(n,k) = 0 if k<0 or if k>n.

T(n,k) = A206735(n,k)*2^k.

T(n,k) = A013609(n,k) - A073424(n,k) .

Example

Triangle begins :
1
0, 2
0, 4, 4
0, 6, 12, 8
0, 8, 24, 32, 16
0, 10, 40, 80, 80, 32
0, 12, 60, 160, 240, 192, 64
0, 14, 84, 280, 560, 672, 448, 128
0, 16, 112, 448, 1120, 1792, 1792, 1024, 256
0, 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512
0, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024

Crossrefs

Cf. A000079, A007318, A013609, A193789, A193790

Sequence in context: A265511 A081236 A338896 * A103328 A344563 A167312

Adjacent sequences: A182056 A182057 A182058 * A182060 A182061 A182062

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Apr 09 2012

Status

approved