A201243 Number of ways to place 2 non-attacking ferses on an n X n board.

0, 4, 28, 102, 268, 580, 1104, 1918, 3112, 4788, 7060, 10054, 13908, 18772, 24808, 32190, 41104, 51748, 64332, 79078, 96220, 116004, 138688, 164542, 193848, 226900, 264004, 305478, 351652, 402868, 459480, 521854, 590368, 665412, 747388, 836710, 933804, 1039108

Offset: 1

Author

Vaclav Kotesovec, Nov 28 2011

Keywords

• nonn
• easy

Comments

Fers is a leaper [1,1].

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, p.415
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A172123, A201244, A201245, A201246, A201247, A201248.

Programs

Magma

I:=[0, 4, 28, 102, 268]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Apr 30 2013

Magma

[(n-1)*(n^3+n^2-4*n+4)/2: n in [1..40]]; // Vincenzo Librandi, Apr 30 2013

Mathematica

Table[(n - 1) (n^3 + n^2 - 4 n + 4) / 2, {n, 100}] (* Vincenzo Librandi, Apr 30 2013 *)
LinearRecurrence[{5,-10,10,-5,1},{0,4,28,102,268},40] (* Harvey P. Dale, Dec 31 2014 *)

Formula

a(n) = 1/2*(n-1)*(n^3 + n^2 - 4n + 4) by C. Poisson, 1990.

G.f.: 2x^2*(x+1)*(x^2-2x-2)/(x-1)^5.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Vincenzo Librandi, Apr 30 2013