A195317 Centered 40-gonal numbers.

1, 41, 121, 241, 401, 601, 841, 1121, 1441, 1801, 2201, 2641, 3121, 3641, 4201, 4801, 5441, 6121, 6841, 7601, 8401, 9241, 10121, 11041, 12001, 13001, 14041, 15121, 16241, 17401, 18601, 19841, 21121, 22441, 23801, 25201, 26641, 28121, 29641, 31201, 32801, 34441, 36121

Offset

1,2

Comments

Also centered tetracontagonal numbers or centered tetrakaicontagonal numbers. Also sequence found by reading the line from 1, in the direction 1, 41, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Semi-axis opposite to A195322 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) = 20*n^2 - 20*n + 1.

Sum_{n>=1} 1/a(n) = Pi*tan(Pi/sqrt(5))/(8*sqrt(5)). - Amiram Eldar, Feb 11 2022

G.f.: -x*(1+38*x+x^2)/(x-1)^3. - R. J. Mathar, May 07 2024

From Elmo R. Oliveira, Nov 15 2024: (Start)

E.g.f.: exp(x)*(20*x^2 + 1) - 1.

a(n) = 2*A069133(n) - 1.

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

Mathematica

Table[20*n^2 - 20*n + 1, {n, 1, 40}] (* Amiram Eldar, Feb 11 2022 *)

Prog

(Magma) [20*n^2 - 20*n + 1: n in [1..50]]; // Vincenzo Librandi, Sep 21 2011
(PARI) a(n)=20*n^2-20*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Bisection of A195148.

Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195316, A195318.

Cf. A195162, A195322.

Sequence in context: A266954 A290589 A191867 * A044292 A044673 A135793

Adjacent sequences: A195314 A195315 A195316 * A195318 A195319 A195320

Keyword

nonn,easy

Author

Omar E. Pol, Sep 16 2011

Status

approved