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, 30997, 32509

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

From Elmo R. Oliveira, Nov 14 2024: (Start)

E.g.f.: exp(x)*(18*x^2 + 1) - 1.

a(n) = 2*A069131(n) - 1.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)

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
(PARI) a(n)=18*n^2-18*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Bisection of A195147.

Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195317, A195318.

Cf. A069131, A195160, A195321.

Sequence in context: A171833 A257117 A033215 * A176549 A118536 A003164

Adjacent sequences: A195313 A195314 A195315 * A195317 A195318 A195319

Keyword

nonn,easy

Author

Omar E. Pol, Sep 16 2011

Status

approved