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

%S 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,

%T 112,32,16,80,288,460,599,440,240,64,16,160,472,1128,1489,1600,1056,

%U 512,128,32,208,976,2152,3914,4457,4120,2480,1088,256

%N 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.

%C Row sums are the powers of 3.

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

%F 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.

%F 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.

%e Triangle begins :

%e 1

%e 2, 1

%e 2, 5, 2

%e 4, 8, 11, 4

%e 4, 20, 25, 24, 8

%e 8, 28, 70, 69, 52, 16

%e 8, 60, 126, 213, 178, 112, 32

%e 16, 80, 288, 460, 599, 440, 240, 64

%e 16, 160, 472, 1128, 1489, 1600, 1056, 512, 128

%e 32, 208, 976, 2152, 3914, 4457, 4120, 2480, 1088, 256

%Y Cf. A016116, A011782, A111297, A000244

%K easy,nonn,tabl

%O 0,2

%A _Philippe Deléham_, Apr 28 2012