OFFSET
1,1
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).
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.
MATHEMATICA
Range[12, 1000, 16] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
16*Range[60]-4 (* or *) LinearRecurrence[{2, -1}, {12, 28}, 60] (* Harvey P. Dale, Nov 16 2025 *)
PROG
(Magma) [16*n - 4: n in [1..60]]; // Vincenzo Librandi, Jul 24 2011
(PARI) a(n)=16*n-4 \\ Charles R Greathouse IV, Jul 10 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Sep 15 2004
STATUS
approved