A111831 Number of partitions of 6*7^n into powers of 7, also equals column 1 of triangle A111830, which shifts columns left and up under matrix 7th power.

1, 7, 154, 16275, 9106461, 28543862991, 521136519414483, 56980036448207052005, 38084892600214854893482284, 158081960770204032330986210466109, 4125860571927530263431055188002578191656

Offset

0,2

Comments

Let q=7; a(n) equals the partitions of (q-1)*q^n into powers of q, or, the coefficient of x^((q-1)*q^n) in 1/Product_{j>=0}(1-x^(q^j)).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..40

Formula

a(n) = [x^(6*7^n)] 1/Product_{j>=0}(1-x^(7^j)).

Prog

(PARI) a(n, q=7)=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(A[n+2, 2]))

Crossrefs

Cf. A111830 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111826 (q=6), A111836 (q=8).

Sequence in context: A279662 A214382 A141835 * A288545 A139226 A220367

Adjacent sequences: A111828 A111829 A111830 * A111832 A111833 A111834

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved