A350405 a(n) is the smallest number which can be represented as the sum of n distinct nonzero n-gonal numbers in exactly n ways, or 0 if no such number exists.

37, 142, 285, 536, 911, 1268, 1909, 2713, 3876, 5179, 6891, 8901, 11190, 14384, 18087, 21697, 27055, 32166, 39111, 46560, 53892, 64412, 73949, 86778, 98202, 113635, 130088, 148051, 167505, 190968, 214955, 240143, 269775, 297615, 331201, 367429, 409179, 451340, 497830

Offset: 3

Author

Ilya Gutkovskiy, Dec 29 2021

Keywords

• nonn

Examples

			For n = 3: 37 = 1 + 15 + 21 = 3 + 6 + 28 = 6 + 10 + 21.
		

Links

• David A. Corneth, Table of n, a(n) for n = 3..102
• Eric Weisstein's World of Mathematics, Polygonal Number

Crossrefs

Cf. A006484, A025443, A057145, A307598, A350207, A350241, A350288.

Programs

Mathematica

Do[i=1;While[b=PolygonalNumber[n,Range@i++];!IntegerQ[t=Min[First/@Select[Tally[Select[Total/@Subsets[b,{n}],#<=Max@b&]],Last@#==n&]]]];Print@t,{n,3,10}] (* Giorgos Kalogeropoulos, Dec 30 2021 *)

Formula

a(n) >= A006484(n). - David A. Corneth, Dec 30 2021

Extensions

a(10)-a(31) from Michael S. Branicky, Dec 29 2021

More terms from David A. Corneth, Dec 30 2021