A255187 29-gonal numbers: a(n) = n*(27*n-25)/2.

0, 1, 29, 84, 166, 275, 411, 574, 764, 981, 1225, 1496, 1794, 2119, 2471, 2850, 3256, 3689, 4149, 4636, 5150, 5691, 6259, 6854, 7476, 8125, 8801, 9504, 10234, 10991, 11775, 12586, 13424, 14289, 15181, 16100, 17046, 18019, 19019, 20046, 21100

Offset: 0

Author

Luciano Ancora, Apr 04 2015

Keywords

• nonn
• easy

Comments

See comments in A255184.

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (27th row of the table).

Links

• Luciano Ancora, Table of n, a(n) for n = 0..1000
• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. similar sequences listed in A255184.

Programs

Mathematica

Table[n (27 n - 25)/2, {n, 40}]
PolygonalNumber[29,Range[0,40]] (* Harvey P. Dale, Jul 25 2021 *)

PARI

a(n)=n*(27*n-25)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: x*(-1 - 26*x)/(-1 + x)^3.

a(n) = A000217(n) + 26*A000217(n-1).

Product_{n>=2} (1 - 1/a(n)) = 27/29. - Amiram Eldar, Jan 22 2021

E.g.f.: exp(x)*(x + 27*x^2/2). - Nikolaos Pantelidis, Feb 06 2023