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Column 5 of table A125800; also equals row sums of matrix power A078122^5.
5

%I #5 Jun 14 2017 00:16:13

%S 1,6,51,861,32856,3013980,690729981,406279238154,625750288074015,

%T 2563196032703643450,28270494794022487841733,

%U 848050124165724284639262951,69769378541879435090796205851249

%N Column 5 of table A125800; also equals row sums of matrix power A078122^5.

%C Triangle A078122 shifts left one column under matrix cube and is related to partitions into powers of 3.

%o (PARI) a(n)=local(p=5,q=3,A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i || j==1, B[i, j]=1, B[i, j]=(A^q)[i-1, j-1]); )); A=B); return(sum(c=0,n,(A^p)[n+1,c+1]))

%Y Cf. A125800, A078122; other columns: A078125, A078124, A125801, A125802.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 10 2006