A198792 Triangle T(n,k), read by rows, given by (0,1,1,0,0,0,0,0,0,0,...) DELTA (1,0,0,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 6, 3, 1, 0, 8, 16, 12, 4, 1, 0, 16, 40, 40, 20, 5, 1, 0, 32, 96, 120, 80, 30, 6, 1, 0, 64, 224, 336, 280, 140, 42, 7, 1, 0, 128, 512, 896, 896, 560, 224, 56, 8, 1, 0, 256, 1152, 2304, 2688, 2016, 1008, 336, 72, 9, 1
Offset: 0
Examples
Triangle begins : 1 0, 1 0, 1, 1 0, 2, 2, 1 0, 4, 6, 3, 1 0, 8, 16, 12, 4, 1 0, 16, 40, 40, 20, 5, 1
Crossrefs
Formula
Sum_{0<=k<=n} T(n,k)*2^k = A063376(n-1).
G.f.: (1-(y+2)*x+y*x^2)/((1-x*y)*(1-x*(y+2))).
T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - 2*T(n-2,k-1) - T(n-2,k-2) for n>2, T(0,0) = T(1,1) = T(2,2) = T(2,1) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 10 2013
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