A113995 - OEIS

%I #7 Jun 13 2017 23:38:45

%S 1,4,16,64,276,1304,6808,39320,250752,1759604,13530928,113522192,

%T 1034613180,10199679712,108334569184,1235056156832,15059906315120,

%U 195775382409972,2705084927865600,39616257445460560,613348477806011476

%N Column 3 of triangle A113993, also equals column 0 of A113983^4.

%e A113983^4, the matrix 4th power of triangle A113983, begins:

%e 1;

%e 4,1;

%e 16,8,1;

%e 64,48,12,1;

%e 276,272,100,16,1;

%e 1304,1576,752,172,20,1;

%e 6808,9664,5592,1624,264,24,1;

%e 39320,63696,42848,14828,3008,376,28,1;

%e 250752,454192,345200,136888,32628,5024,508,32,1; ...

%o (PARI) a(n)=local(A,B);A=Mat(1);for(m=2,n+2,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==1 || j==i,B[i,j]=1, B[i,j]=A[i-1,j-1]+(A^2)[i-2,j-1] );));A=B);(A^4)[n+1,1]

%Y Cf. A113993, A113989 (column 1), A113994 (column 2), A113996 (column 4), A113997 (row sums); A113983.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 12 2005