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

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Keywords

• nonn

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

Crossrefs

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

Programs

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]))

Formula

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