A255185 26-gonal numbers: a(n) = n*(12*n-11).

0, 1, 26, 75, 148, 245, 366, 511, 680, 873, 1090, 1331, 1596, 1885, 2198, 2535, 2896, 3281, 3690, 4123, 4580, 5061, 5566, 6095, 6648, 7225, 7826, 8451, 9100, 9773, 10470, 11191, 11936, 12705, 13498, 14315, 15156, 16021, 16910, 17823, 18760

Offset: 0

Author

Luciano Ancora, Apr 04 2015

Keywords

• nonn
• easy

Comments

See comments in A255184.

Also star 13-gonal number: a(n) = A051865(n) + 13*A000217(n-1).

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (24th row of the table).

Links

• Luciano Ancora, Table of n, a(n) for n = 0..1000
• Luciano Ancora, Polygonal and Pyramidal numbers, Section 1.
• 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

Magma

[n*(12*n-11): n in [0..50]]; // G. C. Greubel, Jul 12 2024

Mathematica

Table[n (12 n - 11), {n, 50}]
PolygonalNumber[26,Range[0,50]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3,-3,1},{0,1,26},50] (* Harvey P. Dale, Feb 02 2017 *)

PARI

a(n)=n*(12*n-11) \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[n*(12*n-11) for n in range(51)] # G. C. Greubel, Jul 12 2024

Formula

G.f.: x*(1 + 23*x)/(1 - x)^3.

a(n) = A000217(n) + 23*A000217(n-1).

Product_{n>=2} (1 - 1/a(n)) = 12/13. - Amiram Eldar, Jan 22 2021

E.g.f.: exp(x)*(x + 12*x^2). - Nikolaos Pantelidis, Feb 05 2023