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

0,2

Links

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

Formula

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

Prog

(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])))

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.

Sequence in context: A058343 A267407 A337296 * A045330 A193203 A259126

Adjacent sequences: A111824 A111825 A111826 * A111828 A111829 A111830

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved