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Search: id:A111836
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| A111836 |
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Number of partitions of 7*8^n into powers of 8, also equals column 1 of triangle A111835, which shifts columns left and up under matrix 8-th power. |
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7
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| 1, 8, 232, 36968, 35593832, 219379963496, 9003699178010216, 2530260913162860295784, 4970141819535151534947497576, 69322146154435681317709098939119208
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OFFSET
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0,2
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COMMENT
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Let q=8; 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^(7*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(A[n+2, 2]))}
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CROSSREFS
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Cf. A111835 (triangle), A002577 (q=2), A078124 (q=3), A111817 (q=4), A111821 (q=5), A111826 (q=6), A111831 (q=7).
Sequence in context: A006919 A013377 A033508 this_sequence A134504 A145418 A067360
Adjacent sequences: A111833 A111834 A111835 this_sequence A111837 A111838 A111839
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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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