A255186 27-gonal numbers: a(n) = n*(25*n-23)/2.

0, 1, 27, 78, 154, 255, 381, 532, 708, 909, 1135, 1386, 1662, 1963, 2289, 2640, 3016, 3417, 3843, 4294, 4770, 5271, 5797, 6348, 6924, 7525, 8151, 8802, 9478, 10179, 10905, 11656, 12432, 13233, 14059, 14910, 15786, 16687, 17613, 18564, 19540

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 (25th 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 (25 n - 23)/2, {n, 40}]

PARI

a(n)=n*(25*n-23)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: x*(-1 - 24*x)/(-1 + x)^3.

a(n) = A000217(n) + 24*A000217(n-1).

Product_{n>=2} (1 - 1/a(n)) = 25/27. - Amiram Eldar, Jan 22 2021

E.g.f.: exp(x)*(x + 25*x^2/2). - Nikolaos Pantelidis, Feb 06 2023