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A303827
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Number of ways of writing n as a sum of powers of 4, each power being used at most 5 times.
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2
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1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 2, 2, 4, 4, 2, 2, 3, 3, 1, 1, 2, 2, 1, 1, 3, 3, 2, 2, 4, 4, 2, 2, 3, 3, 1, 1, 2, 2, 1, 1, 3, 3, 2, 2, 4, 4, 2, 2, 3, 3, 1, 1, 2, 2, 1, 1, 4, 4, 3, 3, 6, 6, 3, 3, 5, 5, 2, 2, 4, 4, 2, 2, 6, 6, 4, 4, 8, 8, 4, 4, 6, 6
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f.: Product_{k>=0} (1-x^(6*4^k))/(1-x^(4^k)).
G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 + x^4 + x^5) * A(x^4). - Ilya Gutkovskiy, Jul 09 2019
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EXAMPLE
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a(17) = 3 because 17=16+1=4+4+4+4+1=4+4+4+1+1+1+1+1.
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
add(b(n-j*4^i, i-1), j=0..min(5, n/4^i))))
end:
a:= n-> b(n, ilog[4](n)):
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MATHEMATICA
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m = 100; A[_] = 1;
Do[A[x_] = (1+x+x^2+x^3+x^4+x^5) * A[x^4] + O[x]^m // Normal, {m}];
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CROSSREFS
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Number of ways of writing n as a sum of powers of b, each power being used at most b+1 times: A117535 (b=3), this sequence (b=4), A303828 (b=5).
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KEYWORD
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AUTHOR
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STATUS
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approved
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