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Search: id:A111831
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| A111831 |
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Number of partitions of 6*7^n into powers of 7, also equals column 1 of triangle A111830, which shifts columns left and up under matrix 7-th power. |
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7
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| 1, 7, 154, 16275, 9106461, 28543862991, 521136519414483, 56980036448207052005, 38084892600214854893482284, 158081960770204032330986210466109, 4125860571927530263431055188002578191656
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Let q=7; a(n) equals the partitions of (q-1)*q^n into powers of q, or, the coefficient of x^((q-1)*q^n) in 1/Product_{j>=0}(1-x^(q^j)).
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FORMULA
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a(n) = [x^(6*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(A[n+2, 2]))}
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CROSSREFS
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Cf. A111830 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111826 (q=6), A111836 (q=8).
Sequence in context: A006761 A144683 A141835 this_sequence A139226 A073605 A115866
Adjacent sequences: A111828 A111829 A111830 this_sequence A111832 A111833 A111834
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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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