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A303825
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Number of ways of writing n as a sum of powers of 7, each power being used at most seven times.
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2
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2, 2, 2, 2, 2, 3
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OFFSET
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0,8
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LINKS
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FORMULA
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G.f.: Product_{k>=0} (1-x^(8*7^k))/(1-x^(7^k)).
a(0)=1; for k>0, a(7*k) = a(k)+a(k-1) and a(7*k+r) = a(k) with r=1,2,3,4,5,6.
G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7) * A(x^7). - Ilya Gutkovskiy, Jul 09 2019
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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*7^i, i-1), j=0..min(7, n/7^i))))
end:
a:= n-> b(n, ilog[7](n)):
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MATHEMATICA
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m = 120; A[_] = 1;
Do[A[x_] = Total[x^Range[0, 7]] A[x^7] + O[x]^m // Normal, {m}];
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PROG
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(Ruby)
def A(k, n)
ary = [1]
(1..n).each{|i|
s = ary[i / k]
s += ary[i / k - 1] if i % k == 0
ary << s
}
ary
end
p A(7, 100)
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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 times: A054390 (b=3), A277872 (b=4), A277873 (b=5), A303824 (b=6), this sequence (b=7).
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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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