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A277873 Number of ways of writing n as a sum of powers of 5, each power being used at most five times. 5
1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 2, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 2, 2, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 2, 2, 3, 1, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Also known as the hyper 5-ary partition sequence, often denoted h_5(n).

Contains A002487 as a subsequence.

LINKS

Timothy B. Flowers, Table of n, a(n) for n = 0..10000

K. Courtright and J. Sellers, Arithmetic properties for hyper m-ary partition functions, Integers, 4 (2004), A6.

Timothy B. Flowers, Extending a Recent Result on Hyper m-ary Partition Sequences, Journal of Integer Sequences, Vol. 20 (2017), #17.6.7.

T. B. Flowers and S. R. Lockard, Identifying an m-ary partition identity through an m-ary tree, Integers, 16 (2016), A10.

FORMULA

G.f.: Product_{j >= 0} (1-x^(6*5^j))/(1-x^(5^j)).

G.f.: Product_{j >= 0} Sum_{k=0..5} x^(k*5^j).

a(0)=1; for k>0, a(5*k) = a(k)+a(k-1) and a(5*k+r) = a(k) with r=1,2,3,4.

EXAMPLE

a(140) = 4 because 140 = 125+5+5+5 = 125+5+5+1+1+1+1+1 = 25+25+25+25+25+5+5+5 = 25+25+25+25+25+5+5+1+1+1+1+1.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,

      add(b(n-j*5^i, i-1), j=0..min(5, n/5^i))))

    end:

a:= n-> b(n, ilog[5](n)):

seq(a(n), n=0..120);  # Alois P. Heinz, May 01 2018

MATHEMATICA

n:=250; r:=3; (* To get up to n-th term, need r such that 5^r < n < 5^(r+1) *) h5 :=  CoefficientList[ Series[ Product[ (1 - q^(6*5^i))/(1 - q^(5^i)) , {i, 0, r}], {q, 0, n} ], q]

CROSSREFS

Cf. A002487, A054390, A277872.

Sequence in context: A177706 A130782 A055457 * A032542 A107038 A236833

Adjacent sequences:  A277870 A277871 A277872 * A277874 A277875 A277876

KEYWORD

nonn

AUTHOR

Timothy B. Flowers, Nov 07 2016

STATUS

approved

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Last modified January 16 15:53 EST 2019. Contains 319195 sequences. (Running on oeis4.)