A010329 -id:A010329 - cp's OEIS frontend

A334013 a(n) is the least integer that is the sum of two nonzero tetrahedral numbers in exactly n ways.

2, 140, 102424, 43322844421220

Offset: 1

Ilya Gutkovskiy, Apr 12 2020

			Let Te(k) denote the k-th tetrahedral number, then
a(1) = Te(1) + Te(1);
a(2) = Te(7) + Te(6) = Te(8) + Te(4);
a(3) = Te(82) + Te(34) = Te(83) + Te(27) = Te(84) + Te(7);
a(4) = Te(60500) + Te(33760) = Te(53311) + Te(47682) = Te(63383) + Te(17423) = Te(63495) + Te(15790);

Eric Weisstein's World of Mathematics, Tetrahedral Number
Index to sequences related to pyramidal numbers

Cf. A000292, A010329, A011541, A053587.

a(4) from Giovanni Resta, Apr 13 2020

A102856 Sum of 1 or 2 distinct tetrahedral numbers.

Original entry on oeis.org

0, 1, 4, 5, 10, 11, 14, 20, 21, 24, 30, 35, 36, 39, 45, 55, 56, 57, 60, 66, 76, 84, 85, 88, 91, 94, 104, 119, 120, 121, 124, 130, 140, 155, 165, 166, 169, 175, 176, 185, 200, 204, 220, 221, 224, 230, 240, 249, 255, 276, 285, 286, 287, 290, 296, 304, 306

Offset: 1

Jud McCranie, Mar 01 2005

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000292 (subsequence), A010329, A104246, A102795-A102800, A102802-A102806, A102855, A102857, A102858, A334013.

Cf. A102801 (sums if 2 distinct positive)

N:= 1000: # for terms <= N
R:= 0:
for i from 1 do
  ti:= i*(i+1)*(i+2)/6;
  if ti > N then break fi;
  for j from 0 to i-1 do
     v:= ti + j*(j+1)*(j+2)/6;
     if v > N then break fi;
     R:= R, v;
  od;
od:
sort(convert({R},list)); # Robert Israel, Jan 16 2024

Module[{nn=12, tetra}, tetra=Table[(n(n+1)(n+2))/6, {n, nn}]; Union[ Total/@ Subsets[tetra, 2]]] (* James C. McMahon, Jan 12 2024 *)

a(1) = 0 prepended by James C. McMahon, Jan 15 2024

cp's OEIS Frontend

A334013 a(n) is the least integer that is the sum of two nonzero tetrahedral numbers in exactly n ways.

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