A172225 Number of ways to place 2 nonattacking wazirs on an n X n board.

0, 2, 24, 96, 260, 570, 1092, 1904, 3096, 4770, 7040, 10032, 13884, 18746, 24780, 32160, 41072, 51714, 64296, 79040, 96180, 115962, 138644, 164496, 193800, 226850, 263952, 305424, 351596, 402810, 459420, 521792, 590304

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

Comments

A wazir is a (fairy chess) leaper [0,1].

References

• Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p. 829.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A036464, A061995, A172132, A172123, A172137.

Programs

Magma

I:=[0, 2, 24, 96, 260]; [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*(n-1)*(n^2+n-4)/2: n in [1..40]]; // Vincenzo Librandi, Apr 30 2013

Mathematica

Table[n (n - 1) (n^2 + n - 4) / 2, {n, 40}] (* Vincenzo Librandi, Apr 30 2013 *)
LinearRecurrence[{5,-10,10,-5,1},{0,2,24,96,260},40] (* Harvey P. Dale, Jun 04 2023 *)

Formula

Explicit formula (Christian Poisson, 1990): a(n) = n*(n-1)*(n^2+n-4)/2.

G.f.: 2*x^2*(2*x^2-7*x-1)/(x-1)^5. - Vaclav Kotesovec, Mar 25 2010

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

a(n) = 2*A239352(n). - R. J. Mathar, Jan 09 2018

a(n) = A232833(n,2). - R. J. Mathar, Apr 11 2024