A254474 30-gonal numbers: a(n) = n*(14*n-13).

0, 1, 30, 87, 172, 285, 426, 595, 792, 1017, 1270, 1551, 1860, 2197, 2562, 2955, 3376, 3825, 4302, 4807, 5340, 5901, 6490, 7107, 7752, 8425, 9126, 9855, 10612, 11397, 12210, 13051, 13920, 14817, 15742, 16695, 17676, 18685, 19722, 20787, 21880

Offset: 0

Author

Luciano Ancora, Apr 04 2015

Keywords

• nonn
• easy

Comments

See comments in A255184.

Also star 15-gonal numbers.

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6 (28th 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

Mathematica

Table[n (14 n - 13), {n, 40}]

PARI

a(n)=n*(14*n-13) \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: x*(-1 - 27*x)/(-1 + x)^3.

a(n) = A000217(n) + 27*A000217(n-1).

a(n) = A051867(n) + 15*A000217(n-1).

Product_{n>=2} (1 - 1/a(n)) = 14/15. - Amiram Eldar, Jan 22 2021

E.g.f.: exp(x)*(x + 14*x^2). - Nikolaos Pantelidis, Feb 05 2023