A195058 Concentric 23-gonal numbers.

0, 1, 23, 47, 92, 139, 207, 277, 368, 461, 575, 691, 828, 967, 1127, 1289, 1472, 1657, 1863, 2071, 2300, 2531, 2783, 3037, 3312, 3589, 3887, 4187, 4508, 4831, 5175, 5521, 5888, 6257, 6647, 7039, 7452, 7867, 8303, 8741, 9200, 9661, 10143, 10627

Offset

0,3

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) = 23*n^2/4 + 19*((-1)^n-1)/8.

From Colin Barker, Sep 16 2012: (Start)

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

G.f.: x*(1 + 21*x + x^2)/((1-x)^3*(1+x)). (End)

Sum_{n>=1} 1/a(n) = Pi^2/138 + tan(sqrt(19/23)*Pi/2)*Pi/sqrt(437). - Amiram Eldar, Jan 17 2023

Mathematica

Table[23n^2/4 + 19((-1)^n - 1)/8, {n, 0, 49}] (* Alonso del Arte, Jan 23 2015 *)
LinearRecurrence[{2, 0, -2, 1}, {0, 1, 23, 47}, 50] (* Harvey P. Dale, Jul 22 2023 *)

Prog

(PARI) a(n)=23*n^2/4+19*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Column 23 of A195040.

Cf. A032527, A032528, A195049, A195149, A195158.

Sequence in context: A090191 A281022 A054821 * A352291 A039374 A043197

Adjacent sequences: A195055 A195056 A195057 * A195059 A195060 A195061

Keyword

nonn,easy

Author

Omar E. Pol, Sep 28 2011

Status

approved