A111836 Number of partitions of 7*8^n into powers of 8, also equals column 1 of triangle A111835, which shifts columns left and up under matrix 8th power.

1, 8, 232, 36968, 35593832, 219379963496, 9003699178010216, 2530260913162860295784, 4970141819535151534947497576, 69322146154435681317709098939119208

Offset

0,2

Comments

Let q=8; 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^(7*8^n)] 1/Product_{j>=0}(1-x^(8^j)).

Prog

(PARI) a(n, q=8)=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. A111835 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111826 (q=6), A111831 (q=7).

Sequence in context: A214351 A303450 A301437 * A288546 A134504 A145418

Adjacent sequences: A111833 A111834 A111835 * A111837 A111838 A111839

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved