A195049 Concentric 21-gonal numbers.

0, 1, 21, 43, 84, 127, 189, 253, 336, 421, 525, 631, 756, 883, 1029, 1177, 1344, 1513, 1701, 1891, 2100, 2311, 2541, 2773, 3024, 3277, 3549, 3823, 4116, 4411, 4725, 5041, 5376, 5713, 6069, 6427, 6804, 7183, 7581, 7981, 8400, 8821, 9261, 9703, 10164

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) = 21*n^2/4 + 17*((-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+19*x+x^2)/((1-x)^3*(1+x)). (End)

Sum_{n>=1} 1/a(n) = Pi^2/126 + tan(sqrt(17/21)*Pi/2)*Pi/sqrt(357). - Amiram Eldar, Jan 17 2023

Maple

A195049:=n->21*n^2/4+17*((-1)^n-1)/8: seq(A195049(n), n=0..100); # Wesley Ivan Hurt, Jan 17 2017

Mathematica

LinearRecurrence[{2, 0, -2, 1}, {0, 1, 21, 43}, 50] (* Amiram Eldar, Jan 17 2023 *)

Prog

(PARI) a(n)=21*n^2/4+17*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Column 21 of A195040.

Cf. A032527, A032528, A195048, A195148, A195149, A195058.

Sequence in context: A041868 A135391 A118569 * A041874 A041872 A041876

Adjacent sequences: A195046 A195047 A195048 * A195050 A195051 A195052

Keyword

nonn,easy

Author

Omar E. Pol, Sep 27 2011

Status

approved