A111832 Number of partitions of 7^n into powers of 7, also equals the row sums of triangle A111830, which shifts columns left and up under matrix 7th power.

1, 2, 9, 205, 24901, 16077987, 58169810617, 1226373476385199, 154912862345527456431, 119679779055077323244243580, 574461679441277269788798742908435, 17346328772332966415272910459727649244337, 3328366331331467859745524303574824288197338547909

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..28

Formula

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

Crossrefs

Cf. A111830, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111827 (q=6), A111837 (q=8). Column 7 of A145515.

Sequence in context: A216692 A367901 A069649 * A114563 A217017 A112311

Adjacent sequences: A111829 A111830 A111831 * A111833 A111834 A111835

Keyword

nonn

Author

Gottfried Helms and Paul D. Hanna, Aug 22 2005

Status

approved