A264997 Number of partitions of n into distinct parts of the form 3^a*5^b.

1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 0, 1, 2, 2, 1, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 3, 3, 2, 4, 3, 1, 3, 3, 3, 3, 3, 3, 4, 4, 2, 4, 3, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 3, 4, 2, 3, 4, 2, 5, 5, 3, 4, 4, 4, 5, 4, 2, 6, 6, 3, 5

Offset

0,10

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 1001 terms from Joseph Myers)

British Mathematical Olympiad 2015/16, Olympiad Round 1, Problem 6, Friday, 27 November 2015.

Formula

G.f.: (1+x)(1+x^3)(1+x^5)(1+x^9)(1+x^15)....

Example

28 = 27 + 1 = 25 + 3 = 15 + 9 + 3 + 1, so a(28) = 3.

Mathematica

nmax = 100; A003593 = Select[Range[nmax], PowerMod[15, #, #] == 0 &]; CoefficientList[Series[Product[(1 + x^(A003593[[k]])), {k, 1, Length[A003593]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Dec 01 2015 *)

Prog

(Haskell)
import Data.MemoCombinators (memo2, list, integral)
a264997 n = a264997_list !! (n-1)
a264997_list = f 0 [] a003593_list where
   f u vs ws'@(w:ws) | u < w = (p' vs u) : f (u + 1) vs ws'
                     | otherwise = f u (vs ++ [w]) ws
   p' = memo2 (list integral) integral p
   p _  0 = 1
   p [] _ = 0
   p (k:ks) m = if m < k then 0 else p' ks (m - k) + p' ks m
-- Reinhard Zumkeller, Dec 18 2015

Crossrefs

Cf. A003593, A264998.

Sequence in context: A240718 A357071 A292518 * A222759 A357072 A024940

Adjacent sequences: A264994 A264995 A264996 * A264998 A264999 A265000

Keyword

easy,nonn,look

Author

Joseph Myers, Nov 29 2015

Status

approved