A195048 Concentric 19-gonal numbers.

0, 1, 19, 39, 76, 115, 171, 229, 304, 381, 475, 571, 684, 799, 931, 1065, 1216, 1369, 1539, 1711, 1900, 2091, 2299, 2509, 2736, 2965, 3211, 3459, 3724, 3991, 4275, 4561, 4864, 5169, 5491, 5815, 6156, 6499, 6859, 7221, 7600, 7981, 8379, 8779, 9196

Offset: 0

Author

Omar E. Pol, Sep 27 2011

Keywords

• nonn
• easy

Comments

Also concentric enneadecagonal numbers.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Column 19 of A195040.

Cf. A032527, A032528, A195047, A195147, A195148, A195049.

Programs

Mathematica

LinearRecurrence[{2,0,-2,1},{0,1,19,39},50] (* Harvey P. Dale, May 17 2016 *)

PARI

a(n)=19*n^2/4+15*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = (19/4)*n^2 + (15/8)*((-1)^n - 1).

From Colin Barker, Sep 16 2012: (Start)

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

G.f.: x*(1 + 17*x + x^2)/((1-x)^3*(1+x)). (End)

Sum_{n>=1} 1/a(n) = Pi^2/114 + tan(sqrt(15/19)*Pi/2)*Pi/sqrt(285). - Amiram Eldar, Jan 17 2023