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Search: id:A111837
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| A111837 |
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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 8-th power. |
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6
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| 1, 2, 10, 298, 53674, 58573738, 409251498922, 19046062579215274, 6071277235712979102634, 13531779463193107731083553706, 214224474679766323250278564215516074
(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^(8^n)] 1/Product_{j>=0}(1-x^(8^j)).
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PROGRAM
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(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])))}
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CROSSREFS
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Cf. A111835, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111827 (q=6), A111832 (q=7).
Sequence in context: A143249 A161181 A073834 this_sequence A092123 A079278 A015178
Adjacent sequences: A111834 A111835 A111836 this_sequence A111838 A111839 A111840
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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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