A182059 - OEIS

%I #6 Feb 22 2013 14:39:46

%S 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,

%T 192,64,0,14,84,280,560,672,448,128,0,16,112,448,1120,1792,1792,1024,

%U 256,0,18,144,672,2016,4032,5376,4608,2304,512

%N 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.

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

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

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

%F 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.

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

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

%e Triangle begins :

%e 1

%e 0, 2

%e 0, 4, 4

%e 0, 6, 12, 8

%e 0, 8, 24, 32, 16

%e 0, 10, 40, 80, 80, 32

%e 0, 12, 60, 160, 240, 192, 64

%e 0, 14, 84, 280, 560, 672, 448, 128

%e 0, 16, 112, 448, 1120, 1792, 1792, 1024, 256

%e 0, 18, 144, 672, 2016, 4032, 5376, 4608, 2304, 512

%e 0, 20, 180, 960, 3360, 8064, 13440, 15360, 11520, 5120, 1024

%Y Cf. A000079, A007318, A013609, A193789, A193790

%K easy,nonn,tabl

%O 0,3

%A _Philippe Deléham_, Apr 09 2012