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

3,1

Comments

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

Links

Table of n, a(n) for n=3..40.

Eric Weisstein's World of Mathematics, Centered Polygonal Number

Formula

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

Example

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

Crossrefs

Cf. A101321, A350209, A350397, A350405.

Sequence in context: A090762 A206337 A161482 * A044428 A044809 A115437

Adjacent sequences: A352972 A352973 A352974 * A352976 A352977 A352978

Keyword

nonn

Author

Ilya Gutkovskiy, 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

Status

approved