A118024 Triangle T, read by rows, T(n,k) = T(n-k)*2^(k*(n-k)) such that column 0 of the matrix square of T equals column 0 of T shifted left: [T^2](n,k) = T(n-k+1,0)*2^(k*(n-k)) for n>=k>=0.
1, 1, 1, 2, 2, 1, 6, 8, 4, 1, 28, 48, 32, 8, 1, 216, 448, 384, 128, 16, 1, 2864, 6912, 7168, 3072, 512, 32, 1, 66656, 183296, 221184, 114688, 24576, 2048, 64, 1, 2760896, 8531968, 11730944, 7077888, 1835008, 196608, 8192, 128, 1, 205824384, 706789376
Offset: 0
Examples
Triangle T begins: 1; 1,1; 2,2,1; 6,8,4,1; 28,48,32,8,1; 216,448,384,128,16,1; 2864,6912,7168,3072,512,32,1; 66656,183296,221184,114688,24576,2048,64,1; ... 2760896,8531968,11730944,7077888,1835008,196608,8192,128,1; ... Matrix square is given by [T^2](n,k) = T(n-k+1,0)*2^(k*(n-k)): 1; 2,1; 6,4,1; 28,24,8,1; 216,224,96,16,1; 2864,3456,1792,384,32,1; ... so that column 0 of T^2 equals column 0 of T shift left 1 place.
Programs
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PARI
{T(n, k)=if(n<0 || k>n,0,if(n==k,1,2^k*sum(j=0, n-1, T(n-1, j)*T(j, k)); ))} \\ Paul D. Hanna, Sep 25 2006
Formula
T(n,k) = A118025(n-k)*2^(k*(n-k)) for n>=k>=0.
Comments