A118024 - OEIS

%I #6 Jun 13 2017 23:43:43

%S 1,1,1,2,2,1,6,8,4,1,28,48,32,8,1,216,448,384,128,16,1,2864,6912,7168,

%T 3072,512,32,1,66656,183296,221184,114688,24576,2048,64,1,2760896,

%U 8531968,11730944,7077888,1835008,196608,8192,128,1,205824384,706789376

%N 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.

%C Column 0 is A118025, where T(n,k) = A118025(n-k)*2^(k*(n-k)).

%F T(n,k) = A118025(n-k)*2^(k*(n-k)) for n>=k>=0.

%e Triangle T begins:

%e 1;

%e 1,1;

%e 2,2,1;

%e 6,8,4,1;

%e 28,48,32,8,1;

%e 216,448,384,128,16,1;

%e 2864,6912,7168,3072,512,32,1;

%e 66656,183296,221184,114688,24576,2048,64,1; ...

%e 2760896,8531968,11730944,7077888,1835008,196608,8192,128,1; ...

%e Matrix square is given by [T^2](n,k) = T(n-k+1,0)*2^(k*(n-k)):

%e 1;

%e 2,1;

%e 6,4,1;

%e 28,24,8,1;

%e 216,224,96,16,1;

%e 2864,3456,1792,384,32,1; ...

%e so that column 0 of T^2 equals column 0 of T shift left 1 place.

%o (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

%Y Cf. A118025 (column 0); A117401 (related triangle); A118022 (variant).

%Y Cf. A123305.

%K nonn,tabl

%O 0,4

%A _Paul D. Hanna_, Apr 10 2006