A195318 Centered 44-gonal numbers.

1, 45, 133, 265, 441, 661, 925, 1233, 1585, 1981, 2421, 2905, 3433, 4005, 4621, 5281, 5985, 6733, 7525, 8361, 9241, 10165, 11133, 12145, 13201, 14301, 15445, 16633, 17865, 19141, 20461, 21825, 23233, 24685, 26181, 27721, 29305, 30933, 32605, 34321, 36081

Offset

1,2

Comments

Sequence found by reading the line from 1, in the direction 1, 45, ..., in the square spiral whose vertices are the generalized tridecagonal numbers A195313. Semi-axis opposite to A195323 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) = 22*n^2 - 22*n + 1.

Sum_{n>=1} 1/a(n) = Pi*tan(3*Pi/(2*sqrt(11)))/(6*sqrt(11)). - Amiram Eldar, Feb 11 2022

Mathematica

Table[22n^2-22n+1, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 45, 133}, 50] (* Harvey P. Dale, Mar 16 2019 *)

Prog

(Magma) [22*n^2 - 22*n + 1: n in [1..50]]; // Vincenzo Librandi, Sep 21 2011
(PARI) a(n)=22*n^2-22*n+1 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Bisection of A195149.

Cf. A003154, A069129, A069133, A069190, A195314, A195315, A195316, A195317.

Sequence in context: A277131 A206209 A098924 * A131011 A336507 A156370

Adjacent sequences: A195315 A195316 A195317 * A195319 A195320 A195321

Keyword

nonn,easy

Author

Omar E. Pol, Sep 16 2011

Status

approved