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, 37885, 39733

Offset: 1

Author

Omar E. Pol, Sep 16 2011

Keywords

• nonn
• easy

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).

Crossrefs

Bisection of A195149.

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

Cf. A069173, A195313, A195323.

Programs

Magma

[22*n^2 - 22*n + 1: n in [1..50]]; // Vincenzo Librandi, Sep 21 2011

Mathematica

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

PARI

a(n)=22*n^2-22*n+1 \\ Charles R Greathouse IV, Jun 17 2017

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

G.f.: -x*(1+42*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)*(22*x^2 + 1) - 1.

a(n) = 2*A069173(n) - 1.

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