A214777 -id:A214777 - cp's OEIS frontend

A065003 Not McNugget numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, 43

Offset: 1

Karl Sabbagh (karl.sabbagh(AT)btinternet.com), Nov 01 2001

A McNugget number has the form 6x + 9y + 20z for nonnegative integers x, y, z.

A214772(a(n)) = 0. - Reinhard Zumkeller, Jul 28 2012

Eric Weisstein, Concise Encyclopedia of Mathematics, p. 1151.

Agustín Moreno Cañadas, Juan David Camacho, and Isaías David Marín Gaviria, Relationships Between Mutations of Brauer Configuration Algebras and Some Diophantine Equations, arXiv:2105.11529 [math.RT], 2021, see p. 2.
Scott Chapman, Christopher O'Neill, Factoring in the Chicken McNugget monoid, arXiv:1709.01606 [math.AC], 2017.
James Grime and Brady Haran, How to order 43 Chicken McNuggets, Numberphile video (2012)
C. U. Jensen and A. Thorup, Gorenstein orders, Journal of Pure and Applied Algebra, Volume 219, Issue 3, March 2015, Pages 551-562. See Example 7.1. - _N. J. A. Sloane_, Jul 22 2014
Eric Weisstein's World of Mathematics, McNugget Numbers.
Wikipedia, Coin problem

Cf. A214777 (complement).

import Data.List (elemIndices)
a065003 n = a065003_list !! n
a065003_list = elemIndices 0 $ map a214772 [0..43]
-- Reinhard Zumkeller, Jul 28 2012

Select[Range[43], Length@FrobeniusSolve[{6, 9, 20}, #] == 0 &] (* Arkadiusz Wesolowski, Feb 20 2013 *)

is(n)=forstep(k=n,6,-20,if(k%3==0, return(0)));n%20>0 \\ Charles R Greathouse IV, May 05 2013

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

Original entry on oeis.org

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

Reinhard Zumkeller, Jul 28 2012

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

			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.

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

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

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

cp's OEIS Frontend

A065003 Not McNugget numbers.

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