A283365 Minimal number of numbers in A000332 = { C(k,4); k=1,2,3,... } whose sum equals n.

0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 2, 3

Offset: 0

Author

M. F. Hasler, Mar 06 2017

Keywords

• nonn

Comments

Analog, for A000332 = {C(n,4)}, of A061336 (for triangular numbers A000217) and A104246 (for tetrahedral numbers A000292).

Links

• R. J. Mathar, Table of n, a(n) for n = 0..10000
• Hyun Kwang Kim, On regular polytope numbers, Proc. Amer. Math. Soc. 131 (2003), p. 65-75. DOI:10.1090/S0002-9939-02-06710-2.

Crossrefs

Cf. A000332 = {C(n,4)}; A061336 (analog for triangular numbers A000217), A104246 (analog for tetrahedral numbers A000292).

Programs

PARI

{a(n,k=4,M=9e9,N=n) = (n <= k || M <= k+1) && return(n); for(m=k,M,binomial(m,k)>n && (M=m) && break); M-- <= k && return(n); my(b=binomial(M,k),c=binomial(M-1,k),NN); forstep( nn=n\b,0,-1, if(N>NN=nn+g(n-nn*b,k,M,N,d),N=NN); n-(nn-1)*b >= (N-nn+1)*c && break); N}

Formula

a(n) <= 8 = a(64) for all n, according to Kim (2003, first row of table "d = 4", p. 74), but this "numerical result" has no "* denoting exact values" (see Remark at end of paper), so it could be incorrect. [Disclaimer added by M. F. Hasler, Sep 22 2022]