%I #19 Sep 22 2022 15:25:08

%S 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,

%T 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,

%U 6,7,1,2,3,4,5,2,3,4,5,6,3,4,5,6,7,2,3

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

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

%H Hyun Kwang Kim, <a href="https://doi.org/10.1090/S0002-9939-02-06710-2">On regular polytope numbers</a>, Proc. Amer. Math. Soc. 131 (2003), p. 65-75. DOI:10.1090/S0002-9939-02-06710-2.

%F 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]

%o (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}

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

%K nonn

%O 0,3

%A _M. F. Hasler_, Mar 06 2017