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

0,3

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).

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

Mathematica

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

Prog

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

Crossrefs

Column 19 of A195040.

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

Sequence in context: A079044 A258016 A217731 * A299964 A041714 A041716

Adjacent sequences: A195045 A195046 A195047 * A195049 A195050 A195051

Keyword

nonn,easy

Author

Omar E. Pol, Sep 27 2011

Status

approved