The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A333529 Number of triples [n,k,m] with n <= k <= m satisfying T_n + T_k = T_m, where T_i = i*(i+1)/2 are the triangular numbers. 4
 0, 1, 1, 1, 2, 2, 1, 2, 3, 2, 3, 3, 2, 5, 3, 1, 4, 4, 3, 5, 5, 2, 3, 4, 4, 5, 5, 3, 6, 6, 1, 3, 5, 6, 7, 5, 2, 5, 6, 3, 6, 6, 3, 8, 9, 2, 3, 4, 6, 8, 6, 3, 6, 11, 5, 6, 5, 2, 7, 7, 2, 9, 5, 3, 11, 6, 3, 6, 11, 6, 5, 5, 2, 9, 9, 6, 11, 6, 3, 7, 7, 2, 7, 12, 6, 5, 7, 3, 10, 16, 6, 6, 5, 6, 6, 3, 4, 12, 12, 5, 6, 6, 3, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS a(n)=1 if n is in A068194. - Robert Israel, Apr 03 2020 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE There is a list of all triples (including those with 0 < k < n) with n <= 16 in A309507. MAPLE with(numtheory): A:=[]; M:=150; ct:=Array(0..M, 0): for n from 1 to M do TT:=n*(n+1); dlis:=divisors(TT);   for d in dlis do if (d mod 2) = 1 then e := TT/d; mi:=min(d, e); ma:=max(d, e); k:=(ma-mi-1)/2; m:=(ma+mi-1)/2; # skip if k=n then     ct[n]:=ct[n]+1;     lprint(n, k, m);     fi; fi; od: od: [seq(ct[n], n=1..M)]; # alternative: f:= proc(n) local t, t0, r, dmax, divs;     t:= n*(n+1);     r:= padic:-ordp(t, 2);     t0:= t/2^r;     dmax:= floor((sqrt(8*t+1)-1)/2-n);     divs:= numtheory:-divisors(t0);     nops(select(`<=`, divs, dmax)) + nops(select(`<=`, divs, dmax/2^r)) end proc: map(f, [\$1..200]); # Robert Israel, Apr 03 2020 MATHEMATICA T[n_] := n(n+1)/2; r[n_] := Reduce[n <= k <= m && T[n] + T[k] == T[m], {k, m}, Integers]; a[n_] := Module[{rn = r[n], r0}, r0 = rn[[0]]; Which[r0 === Or, Length[rn], r0 === And, 1, rn === False, 0, True, Print["error ", n, " ", rn]]]; Array[a, 100] (* Jean-François Alcover, Jun 08 2020 *) CROSSREFS A309507 counts all triples with k>0. Cf. A000217, A068194. Sequence in context: A219644 A193676 A029291 * A022872 A091423 A221914 Adjacent sequences:  A333526 A333527 A333528 * A333530 A333531 A333532 KEYWORD nonn,look AUTHOR N. J. A. Sloane, Mar 31 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)