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Search: id:A111817
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| A111817 |
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Number of partitions of 3*4^n into powers of 4, also equals column 1 of triangle A078536, which shifts columns left and up under matrix 4-th power. |
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6
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| 1, 4, 28, 524, 29804, 5423660, 3276048300, 6744720496300, 48290009081437356, 1221415413140406958252, 110523986015743458745929900, 36150734459755630877180158951596
(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=4; 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^(3*4^n)] 1/Product_{j>=0}(1-x^(4^j)).
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PROGRAM
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(PARI) {a(n, q=4)=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. A078536 (triangle), A002577 (q=2), A078124 (q=3), A111821 (q=5), A111826 (q=6), A111831 (q=7), A111836 (q=8).
Sequence in context: A155105 A132685 A086812 this_sequence A134048 A091969 A101346
Adjacent sequences: A111814 A111815 A111816 this_sequence A111818 A111819 A111820
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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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