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A005706
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Number of partitions of 5n into powers of 5.
(Formerly M0519)
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10
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1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 82, 89, 96, 103, 110, 119, 128, 137, 146, 155, 166, 177, 188, 199, 210, 223, 236, 249, 262, 275, 290, 305, 320, 335, 350, 368, 386, 404, 422, 440, 461, 482, 503, 524, 545
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OFFSET
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0,2
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COMMENTS
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Euler transform of [2,0,0,0,1,0,0,0,0,...] with 1's at 5^n. - Michael Somos, Mar 16 2004
Partial sums of number of partitions of n into powers of 5. - Michael Somos, Mar 16 2004
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REFERENCES
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R. K. Guy, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = a(n-1) + a([n/5]).
a(n) = [x^(5*n)] Product_{k>=0} 1/(1 - x^(5^k)). - Ilya Gutkovskiy, Jun 05 2017
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = a[n - 1] + a[Floor[n/5]]; Table[a@ n, {n, 0, 60}] (* Michael De Vlieger, Mar 25 2016 *)
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PROG
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(PARI) a(n)=if(n<1, n==0, a(n-1)+a(n\5))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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