A102855 - OEIS

%I #11 Aug 05 2022 07:42:42

%S 1,-1,-1,1,2,-1,-1,-1,-1,1,2,-1,-1,2,3,-1,-1,-1,-1,1,2,-1,-1,2,3,-1,

%T -1,-1,-1,2,3,-1,-1,3,1,2,-1,-1,2,3,-1,-1,-1,-1,2,3,-1,-1,3,4,-1,-1,

%U -1,-1,2,1,2,-1,3,2,3,-1,-1,-1,3,2,3,-1,4,3,4,-1,-1,-1,-1,2,3,-1,-1

%N Minimal number of distinct nonzero tetrahedral numbers needed to represent n, or -1 if no such representation is possible.

%H Robert Israel, <a href="/A102855/b102855.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 100; # for a(1)..a(N)

%p ft:= t -> t*(t+1)*(t+2)/6:

%p tets:= map(ft, [$1..floor((6*N)^(1/3))]:

%p f:= proc(n,tmax) option remember;

%p    local res, s;

%p    if member(n, tets) and n < tmax then return 1 fi;

%p    min(seq(1 + procname(n-s,s), s=select(`<`,tets,min(n,tmax))));

%p end proc:

%p subs(infinity=-1,map(f, [$1..N],infinity)); # _Robert Israel_, Dec 29 2019

%t M = 100; (* number of terms *)

%t ft[t_] := t(t+1)(t+2)/6;

%t tets = ft /@ Range[1, Floor[(6M)^(1/3)]];

%t f[n_, tmax_] := f[n, tmax] = If[MemberQ[tets, n] && n < tmax, 1, Min[ Table[1 + f[n-s, s], {s, Select[tets, # < Min[n, tmax]&]}]]];

%t f[#, Infinity]& /@ Range[1, M] /. Infinity -> -1 (* _Jean-François Alcover_, Aug 05 2022, after _Robert Israel_ *)

%Y Cf. A104246, A102795-A102806, A102856-A102858.

%K sign

%O 1,5

%A _Jud McCranie_, Mar 01 2005