A283370 Minimal number of terms required to write n as sum of numbers in A000389 = { C(k,5); k=1,2,3,... } (with repetitions allowed).

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

Offset: 0

Author

M. F. Hasler, Mar 06 2017

Keywords

• nonn

Comments

Analog, for A000389 = {C(n,5)}, of A061336 (for triangular numbers A000217 = {C(n,2)}), A104246 (for tetrahedral numbers A000292 = {C(n,3)}) and A283365 (for A000332 = {C(n,4)}).

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 A000217), A104246 (analog for A000292), A283365 (analog for A000332).

Programs

PARI

{a(n,k=5,M=9e9,N=n) = n>k || 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+a(n-nn*b,k,M,N),N=NN); n-(nn-1)*b >= (N-nn+1)*c && break); N}

Formula

a(n) <= 10 = a(220) for all n, according to Kim (2003, p. 74, first row of table "d = 5"), 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]