A195315 Centered 32-gonal numbers.

1, 33, 97, 193, 321, 481, 673, 897, 1153, 1441, 1761, 2113, 2497, 2913, 3361, 3841, 4353, 4897, 5473, 6081, 6721, 7393, 8097, 8833, 9601, 10401, 11233, 12097, 12993, 13921, 14881, 15873, 16897, 17953, 19041, 20161, 21313, 22497, 23713, 24961, 26241

Offset

1,2

Comments

Sequence found by reading the line from 1, in the direction 1, 33, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. Semi-axis opposite to A016802 in the same spiral.

Links

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

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

Formula

a(n) = 16*n^2 - 16*n + 1.

G.f.: -x*(1 + 30*x + x^2) / (x-1)^3. - R. J. Mathar, Sep 18 2011

Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(3)*Pi/4)/(8*sqrt(3)). - Amiram Eldar, Feb 11 2022

Mathematica

Table[16*n^2 - 16*n + 1, {n, 1, 41}] (* Amiram Eldar, Feb 11 2022 *)
LinearRecurrence[{3, -3, 1}, {1, 33, 97}, 50] (* Harvey P. Dale, Feb 11 2024 *)

Prog

(Magma) [(16*n^2-16*n+1): n in [1..50]]; // Vincenzo Librandi, Sep 19 2011
(PARI) a(n)=16*n^2-16*n+1 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Bisection of A195146.

Cf. A003154, A069129, A069133, A069190, A195314, A195316, A195317, A195318.

Sequence in context: A098923 A044220 A044601 * A098441 A032650 A284986

Adjacent sequences: A195312 A195313 A195314 * A195316 A195317 A195318

Keyword

nonn,easy

Author

Omar E. Pol, Sep 16 2011

Status

approved