A195316 - OEIS

A195316

Centered 36-gonal numbers.

1, 37, 109, 217, 361, 541, 757, 1009, 1297, 1621, 1981, 2377, 2809, 3277, 3781, 4321, 4897, 5509, 6157, 6841, 7561, 8317, 9109, 9937, 10801, 11701, 12637, 13609, 14617, 15661, 16741, 17857, 19009, 20197, 21421, 22681, 23977, 25309, 26677, 28081, 29521

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OFFSET

1,2

COMMENTS

Sequence found by reading the line from 1, in the direction 1, 37, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Semi-axis opposite to A195321 in the same spiral.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

John Elias, Illustration of initial terms.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 18*n^2 - 18*n + 1.

G.f.: -x*(1 + 34*x + x^2) / (x-1)^3. - R. J. Mathar, Sep 18 2011

Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(7)*Pi/6)/(6*sqrt(7)). - Amiram Eldar, Feb 11 2022

MATHEMATICA

Table[18*n^2 - 18*n + 1, {n, 1, 40}] (* Amiram Eldar, Feb 11 2022 *)

PROG

(Magma) [(18*n^2-18*n+1): n in [1..50]]; // Vincenzo Librandi, Sep 19 2011