A241766 Number of partitions of n into parts of the form 3^k - 2^k, cf. A001047.

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 10, 10, 11, 12, 12, 12, 13, 14, 15, 15, 15, 16, 17, 18, 18, 18, 19, 20, 21, 21, 21, 22, 23, 24, 24, 25, 26, 27, 28, 28, 29, 30, 31, 33, 33, 34, 35, 36, 38, 38

Offset: 0

Author

Reinhard Zumkeller, Apr 28 2014

Keywords

• nonn

Examples

			A001047(1..4) = {1, 5, 19, 65}:
a(18) = #{5+5+5+1+1+1, 5+5+8x1, 5+13x1, 18x1} = 4;
a(19) = #{19, 5+5+5+1+1+1+1, 5+5+9x1, 5+14x1, 19x1} = 5;
a(20) = #{19+1, 5+5+5+5, 5+5+5+5x1, 5+5+10x1, 5+15x1, 20x1} = 6;
a(21) = #{19+1+1, 5+5+5+5+1, 5+5+5+6x1, 5+5+11x1, 5+16x1, 21x1} = 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001047, A241759.

Programs

Haskell

a241766 = p $ tail a001047_list where
   p _          0 = 1
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - x^(3^k-2^k)), {k, 1, Floor[Log[nmax]/Log[2]] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 24 2017 *)

Formula

G.f.: Product_{k>=1} 1/(1 - x^(3^k-2^k)). - Ilya Gutkovskiy, Jan 23 2017