A195147 - OEIS

A195147

Concentric 18-gonal numbers.

0, 1, 18, 37, 72, 109, 162, 217, 288, 361, 450, 541, 648, 757, 882, 1009, 1152, 1297, 1458, 1621, 1800, 1981, 2178, 2377, 2592, 2809, 3042, 3277, 3528, 3781, 4050, 4321, 4608, 4897, 5202, 5509, 5832, 6157, 6498, 6841, 7200, 7561, 7938, 8317, 8712, 9109

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OFFSET

0,3

COMMENTS

Concentric octadecagonal numbers or concentric octakaidecagonal numbers.

Sequence found by reading the line from 0, in the direction 0, 18, ..., and the same line from 1, in the direction 1, 37, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Main axis, perpendicular to A027468 in the same spiral.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

G.f.: -x*(1+16*x+x^2) / ( (1+x)*(x-1)^3 ). - R. J. Mathar, Sep 18 2011

From Vincenzo Librandi, Sep 27 2011: (Start)

a(n) = (18*n^2 + 7*(-1)^n - 7)/4;

a(n) = -a(n-1) + 9*n^2 - 9*n + 1. (End)

Sum_{n>=1} 1/a(n) = Pi^2/108 + tan(sqrt(7)*Pi/6)*Pi/(6*sqrt(7)). - Amiram Eldar, Jan 17 2023

MATHEMATICA

LinearRecurrence[{2, 0, -2, 1}, {0, 1, 18, 37}, 50] (* Amiram Eldar, Jan 17 2023 *)

PROG