A111837 Number of partitions of 8^n into powers of 8, also equals the row sums of triangle A111835, which shifts columns left and up under matrix 8th power.

1, 2, 10, 298, 53674, 58573738, 409251498922, 19046062579215274, 6071277235712979102634, 13531779463193107731083553706, 214224474679766323250278564215516074, 24390479071277895100812271376578637910371242, 20173309182842708837666031701435147789403500172143530

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..45

Crossrefs

Cf. A111835, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111827 (q=6), A111832 (q=7). Column 8 of A145515.

Programs

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(sum(k=0,n,A[n+1,k+1])))

Formula

a(n) = [x^(8^n)] 1/Product_{j>=0} (1-x^(8^j)).