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%I #6 Feb 22 2013 14:40:27
%S 1,2,4,3,10,8,4,18,28,16,5,28,64,72,32,6,40,120,200,176,64,7,54,200,
%T 440,576,416,128,8,70,308,840,1456,1568,960,256,9,88,448,1456,3136,
%U 4480,4096,2176,512,10,108,624,2352,6048,10752,13056,10368,4864
%N 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.
%C Row sums are A134931(n).
%C Diagonal sums are A140253(n).
%C Compare this sequence with A207627.
%C Column k is divisible by 2^k.
%F T(n,0) = n+1.
%F T(n,1) = 2*T(n,0) + T(n-1,1).
%F T(n,k) = 2*T(n-1,k-1) + T(n-1,k) for k>1.
%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) with T(0,0) = 1, T(1,0) = 2, T(1,1) = 4.
%F G.f.: (1+2*y*x)/(1-2*(1+y)*x+(1+2*y)*x^2).
%e Triangle begins :
%e 1
%e 2, 4
%e 3, 10, 8
%e 4, 18, 28, 16
%e 5, 28, 64, 72, 32
%e 6, 40, 120, 200, 176, 64
%e 7, 54, 200, 440, 576, 416, 128
%e 8, 70, 308, 840, 1456, 1568, 960, 256
%e 9, 88, 448, 1456, 3136, 4480, 4096, 2176, 512
%e 10, 108, 624, 2352, 6048, 10752, 13056, 10368, 4864, 1024
%Y Cf. A207627
%K easy,nonn,tabl
%O 0,2
%A _Philippe Deléham_, Feb 25 2012
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