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Search: id:A078537
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| A078537 |
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Number of partitions of 4^n into powers of 4 (without regard to order). |
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+0
10
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| 1, 2, 6, 46, 1086, 79326, 18583582, 14481808030, 38559135542174, 357934565638890910, 11766678027350761752990, 1387043469046575118555443614, 592264246356176268834689653440926
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OFFSET
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0,2
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COMMENT
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Conjecture: a(n) = sum of the n-th row of lower triangular matrix A078536.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..20
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FORMULA
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a(n) = coefficient of x^(4^n) in power series expansion of 1/[(1-x)(1-x^4)(1-x^16)...(1-x^(4^k))...].
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EXAMPLE
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a(2) = 6 since partitions of 4^2 into powers of 4 are: {16; 4+4+4+4; 4+4+4+1+1+1+1; 4+4+1+1+1+1+1+1+1+1; 4+1+1+1+1+1+1+1+1+1+1+1+1; 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1}.
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = a[n - 1] + a[Floor[n/4]]; b = Table[ a[n], {n, 0, 4^9}]; Table[ b[[4^n + 1]], {n, 0, 9}]
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CROSSREFS
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Cf. A002577, A078125, A078536.
Sequence in context: A052811 A078603 A001587 this_sequence A145502 A072444 A052596
Adjacent sequences: A078534 A078535 A078536 this_sequence A078538 A078539 A078540
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2002
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EXTENSIONS
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Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 01 2002
More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 11 2008
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