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A277872
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Number of ways of writing n as a sum of powers of 4, each power being used at most four times.
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6
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1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 2, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 4, 3, 3, 3, 5, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 5, 3, 3, 3, 4, 1
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OFFSET
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0,5
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COMMENTS
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Also known as the hyper 4-ary partition sequence, often denoted h_4(n).
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LINKS
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FORMULA
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G.f.: Product((1-x^(5*4^j))/(1-x^(4^j))), j=0..infinity).
G.f.: Product(1+x^(4^j)+x^(2*4^j)+x^(3*4^j)+x^(4*4^j), j=0..infinity).
a(0)=1 and for n>0, a(4n)=a(n)+a(n-1), a(4n+r)=a(n) for r=1,2,3.
G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 + x^4) * A(x^4). - Ilya Gutkovskiy, Jul 09 2019
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EXAMPLE
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a(72) = 4 because 72 = 64+4+4 = 64+4+1+1+1+1 = 16+16+16+16+4+4 = 16+16+16+16+4+1+1+1+1.
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MATHEMATICA
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n:=250;
r:=3;
(* To get up to n-th term, need r such that 4^r < n < 4^(r+1) *)
h4 := CoefficientList[ Series[ Product[ (1 - q^(5*4^i))/(1 - q^(4^i)) , {i, 0, r}], {q, 0, n} ], q]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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