A352975 a(n) is the smallest number which can be represented as the sum of n distinct centered n-gonal numbers in exactly n ways, or -1 if no such number exists.

96, 192, 330, 504, 840, 1304, 1872, 2910, 3971, 5340, 6851, 8932, 11700, 14496, 18258, 22410, 27265, 32620, 39606, 47124, 55545, 65448, 76050, 87854, 101925, 116956, 134125, 152340, 173538, 195424, 220473, 246942, 276570, 306756, 340918, 377644, 418821, 462720

Offset: 3

Author

Ilya Gutkovskiy, Apr 13 2022

Keywords

• nonn

Comments

If a(n) exists, then n divides a(n). - Thomas Scheuerle, Apr 13 2022

Examples

			For n = 3: 96 = 1 + 10 + 85 = 1 + 31 + 64 = 19 + 31 + 46.
		

Links

• Eric Weisstein's World of Mathematics, Centered Polygonal Number

Crossrefs

Cf. A101321, A350209, A350397, A350405.

Formula

a(n) >= n*binomial(n + 2, 3) + n, if a(n) exists. - Thomas Scheuerle, Apr 13 2022

Extensions

a(10)-a(16) from Thomas Scheuerle, Apr 13 2022

a(17)-a(40) from Michael S. Branicky, May 19 2022