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

%I A214772 #15 Feb 16 2025 08:33:18
%S A214772 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,
%T A214772 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,
%U A214772 3,5,2,3,6,2,4,5,3,3,7,2,5,6,3,4,7,3
%N A214772 Number of partitions of n into parts 6, 9 or 20.
%C A214772 a(A065003(n)) = 0; a(A214777(n)) > 0.
%H A214772 Reinhard Zumkeller, <a href="/A214772/b214772.txt">Table of n, a(n) for n = 0..1000</a>
%H A214772 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/McNuggetNumber.html">McNugget Numbers</a>.
%H A214772 Wikipedia, <a href="http://en.wikipedia.org/wiki/Coin_problem">Coin problem</a>
%F A214772 G.f. 1/((1-x^6)*(1-x^9)*(1-x^20)). - _R. J. Mathar_, Jul 30 2012
%e A214772 a(10) = 0, cf. A065003(8) = 10;
%e A214772 a(20) = #{20} = 1;
%e A214772 a(30) = #{6+6+6+6+6, 6+6+9+9} = 2;
%e A214772 a(40) = #{20+20} = 1;
%e A214772 a(50) = #{5*6+20, 6+6+9+9+20} = 2;
%e A214772 a(60) = #{10*6, 7*6+9+9, 4*6+4*9, 6+6*9, 20+20+20} = 5;
%e A214772 a(70) = #{5*6+20+20, 6+6+9+9+20+20} = 2
%e A214772 a(80) = #{10*6+20, 7*6+9+9+20, 4*6+4*9+20, 6+6*99+20, 4*20} = 5;
%e A214772 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;
%e A214772 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.
%o A214772 (Haskell)
%o A214772 a214772 = p [6, 9, 20] where
%o A214772    p _      0 = 1
%o A214772    p []     _ = 0
%o A214772    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
%K A214772 nonn,easy
%O A214772 0,19
%A A214772 _Reinhard Zumkeller_, Jul 28 2012