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A111827
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Number of partitions of 6^n into powers of 6, also equals the row sums of triangle A111825, which shifts columns left and up under matrix 6-th power.
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6
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1, 2, 8, 134, 10340, 3649346, 6188114528, 52398157106366, 2277627698797283420, 518758596372421679994170, 628925760908337480420110203736, 4109478867142143642923124190955500214
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..30
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FORMULA
| a(n) = [x^(6^n)] 1/Product_{j>=0}(1-x^(6^j)).
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PROG
| (PARI) {a(n, q=6)=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
| Cf. A111825, A002577 (q=2), A078125 (q=3), A078537 (q=4), A111822 (q=5), A111832 (q=7), A111837 (q=8). Column 6 of A145515.
Sequence in context: A058891 A184945 A058343 * A045330 A193203 A140050
Adjacent sequences: A111824 A111825 A111826 * A111828 A111829 A111830
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KEYWORD
| nonn
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AUTHOR
| Gottfried Helms (helms(AT)uni-kassel.de) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 22 2005
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