A214772 Number of partitions of n into parts 6, 9 or 20.

1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 1, 0, 0, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 2, 2, 1, 1, 3, 0, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 4, 1, 3, 3, 2, 2, 5, 1, 3, 4, 2, 3, 5, 2, 3, 5, 2, 3, 6, 2, 4, 5, 3, 3, 7, 2, 5, 6, 3, 4, 7, 3

Offset: 0

Author

Reinhard Zumkeller, Jul 28 2012

Keywords

• nonn
• easy

Comments

a(A065003(n)) = 0; a(A214777(n)) > 0.

Examples

			a(10) = 0, cf. A065003(8) = 10;
a(20) = #{20} = 1;
a(30) = #{6+6+6+6+6, 6+6+9+9} = 2;
a(40) = #{20+20} = 1;
a(50) = #{5*6+20, 6+6+9+9+20} = 2;
a(60) = #{10*6, 7*6+9+9, 4*6+4*9, 6+6*9, 20+20+20} = 5;
a(70) = #{5*6+20+20, 6+6+9+9+20+20} = 2
a(80) = #{10*6+20, 7*6+9+9+20, 4*6+4*9+20, 6+6*99+20, 4*20} = 5;
a(90) = #{15*6, 12*6+9+9, 9*6+4*9, 6*6+6*99, 5*6+3*20, 3*6+8*9, 6+6+9+9+3*20, 10*9} = 8;
a(100) = #{10*6+2*20, 7*6+9+9+2*20, 4*6+4*9+2*20, 6+6*9+2*20, 5*20} = 5.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, McNugget Numbers.
• Wikipedia, Coin problem

Programs

Haskell

a214772 = p [6, 9, 20] where
   p _      0 = 1
   p []     _ = 0
   p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

Formula

G.f. 1/((1-x^6)*(1-x^9)*(1-x^20)). - R. J. Mathar, Jul 30 2012