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Search: id:A111832
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| A111832 |
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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 7-th power. |
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5
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| 1, 2, 9, 205, 24901, 16077987, 58169810617, 1226373476385199, 154912862345527456431, 119679779055077323244243580, 574461679441277269788798742908435
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = [x^(7^n)] 1/Product_{j>=0}(1-x^(7^j)).
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PROGRAM
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(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])))}
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CROSSREFS
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Cf. A111830, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111827 (q=6), A111837 (q=8).
Adjacent sequences: A111829 A111830 A111831 this_sequence A111833 A111834 A111835
Sequence in context: A041795 A123625 A069649 this_sequence A114563 A112311 A067564
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KEYWORD
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nonn
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AUTHOR
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Gottfried Helms (helms(AT)uni-kassel.de) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 22 2005
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