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A283365 Minimal number of numbers in A000332 = { C(k,4); k=1,2,3,... } whose sum equals n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Analog, for A000332 = {C(n,4)}, of A061336 (for triangular numbers A000217) and A104246 (for tetrahedral numbers A000292).
LINKS
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Mar 06 2017
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)