A098502 a(n) = 16*n - 4.

12, 28, 44, 60, 76, 92, 108, 124, 140, 156, 172, 188, 204, 220, 236, 252, 268, 284, 300, 316, 332, 348, 364, 380, 396, 412, 428, 444, 460, 476, 492, 508, 524, 540, 556, 572, 588, 604, 620, 636, 652, 668, 684, 700, 716, 732, 748, 764, 780, 796, 812, 828, 844

Offset: 1

Author

Ralf Stephan, Sep 15 2004

Keywords

• nonn
• easy

Comments

For n > 3, the number of squares on the infinite 4-column chessboard at <= n knight moves from any fixed start point.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..5000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).
• Index entries for sequences which agree for a long time but are different.

Crossrefs

Cf. A004767, A008590, A017113, A017137, A017629, A098498, A158953.

Programs

Magma

[16*n - 4: n in [1..60]]; // Vincenzo Librandi, Jul 24 2011

Mathematica

Range[12, 1000, 16] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)

PARI

a(n)=16*n-4 \\ Charles R Greathouse IV, Jul 10 2016

Formula

G.f.: 4*x*(3+x)/(1-x)^2. - Colin Barker, Jan 09 2012

Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi + log(3 - 2*sqrt(2)))/(16*sqrt(2)). - Amiram Eldar, Sep 01 2024

From Elmo R. Oliveira, Apr 03 2025: (Start)

E.g.f.: 4*(exp(x)*(4*x - 1) + 1).

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

a(n) = 4*A004767(n-1) = 2*A017137(n-1) = A017113(2*n-1). (End)