A111827 Number of partitions of 6^n into powers of 6, also equals the row sums of triangle A111825, which shifts columns left and up under matrix 6th power.

1, 2, 8, 134, 10340, 3649346, 6188114528, 52398157106366, 2277627698797283420, 518758596372421679994170, 628925760908337480420110203736, 4109478867142143642923124190955500214

Offset: 0

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..52

Crossrefs

Cf. A111825, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111832 (q=7), A111837 (q=8). Column 6 of A145515.

Programs

PARI

a(n,q=6)=local(A=Mat(1),B);if(n<0,0, for(m=1,n+2,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(k=0,n,A[n+1,k+1])))

Formula

a(n) = [x^(6^n)] 1/Product_{j>=0}(1-x^(6^j)).