A234004 Smallest number which is the sum of two positive triangular numbers (A000217) in at least n ways.

2, 16, 81, 471, 1056, 1381, 6906, 6906, 17956, 34531, 40056, 40056, 200281, 200281, 200281, 200281, 520731, 520731, 1001406, 1001406, 1482081, 1482081, 1482081, 1482081, 7410406, 7410406, 7410406, 7410406, 7410406, 7410406, 7410406, 7410406

Offset

1,1

Links

Donovan Johnson, Table of n, a(n) for n = 1..216

Example

2 = 1+1; 16 = 1+15 = 6+10; 81 = 3+78 = 15+66 = 36+45.

Mathematica

poly[n_, k_]:=n (n-1)(k-2)/2+n; nn=10^5; order=3; t2=Table[0, {nn}]; n2=Floor[(-4+#+Sqrt[(-4+#)^2+8 (-2+#) nn])/(2 (-2+#))&[order]]; Do[r=Plus@@poly[{a, b}, order]; If[r<=nn, t2[[r]]++], {a, n2}, {b, a, n2}]; t={}; n=1; While[a=Position[t2, _?(#>=n&), 1, 1]; a!={}, AppendTo[t, a[[1, 1]]]; n++]; t (* after T. D. Noe (A048610) *)

Crossrefs

Cf. A000217, A048610, A199809, A052346, A053587.

Sequence in context: A045905 A012680 A012684 * A053587 A052346 A207482

Adjacent sequences: A234001 A234002 A234003 * A234005 A234006 A234007

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, Dec 18 2013

Status

approved