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

3,1

Links

David A. Corneth, Table of n, a(n) for n = 3..102

Eric Weisstein's World of Mathematics, Polygonal Number

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A013522 A142498 A337258 * A158591 A262318 A262921

Adjacent sequences: A350402 A350403 A350404 * A350406 A350407 A350408

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2021

Extensions

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

More terms from David A. Corneth, Dec 30 2021

Status

approved