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

0,3

Comments

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

Links

Table of n, a(n) for n=0..86.

Hyun Kwang Kim, On regular polytope numbers, Proc. Amer. Math. Soc. 131 (2003), p. 65-75. DOI:10.1090/S0002-9939-02-06710-2.

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]

Prog

(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}

Crossrefs

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

Sequence in context: A338484 A338493 A280053 * A053824 A033925 A358012

Adjacent sequences: A283362 A283363 A283364 * A283366 A283367 A283368

Keyword

nonn

Author

M. F. Hasler, Mar 06 2017

Status

approved