%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