OFFSET
1,2
COMMENTS
A 5 X 5 board, for example, is numbered with the square spiral:
.
21--22--23--24--25
|
20 7---8---9--10
| | |
19 6 1---2 11
| | | |
18 5---4---3 12
| |
17--16--15--14--13
.
A fers is a (1,1)-leaper and can move one square diagonally.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Stephen Emmerson and Geoff Foster, A glossary of fairy chess definitions, British Chess Problem Society, 2018.
Wikipedia, Ferz
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
a(n) = (4n^2-9n+6)*[n is odd] + (4n^2-11n+9)*[n is even] where [] is the Iverson bracket.
From Colin Barker, May 23 2019: (Start)
G.f.: x*(1 + 2*x + 10*x^2 + 10*x^3 + 9*x^4) / ((1 - x)^3*(1 + x)^2).
a(n) = (3/2)*(5+(-1)^n) - (10+(-1)^n)*n + 4*n^2.
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.
(End)
E.g.f.: (1/2)*exp(-x)*(3 + 2*x + exp(2*x)*(15 - 12*x + 8*x^2)) - 9. - Stefano Spezia, Aug 17 2019
MATHEMATICA
Table[(3/2) (5 + (-1)^n) - (10 + (-1)^n) n + 4 n^2, {n, 60}] (* Vincenzo Librandi, Aug 01 2019 *)
PROG
(PARI) Vec(x*(1 + 2*x + 10*x^2 + 10*x^3 + 9*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^40)) \\ Colin Barker, May 23 2019
(Magma) [(3/2)*(5+(-1)^n) - (10+(-1)^n)*n + 4*n^2: n in [1..50]]; // Vincenzo Librandi, Aug 01 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sangeet Paul, May 23 2019
STATUS
approved