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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.
6
1, 2, 9, 205, 24901, 16077987, 58169810617, 1226373476385199, 154912862345527456431, 119679779055077323244243580, 574461679441277269788798742908435, 17346328772332966415272910459727649244337, 3328366331331467859745524303574824288197338547909
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved