A172137 Number of ways to place 2 nonattacking zebras on an n X n board.

0, 6, 36, 112, 276, 582, 1096, 1896, 3072, 4726, 6972, 9936, 13756, 18582, 24576, 31912, 40776, 51366, 63892, 78576, 95652, 115366, 137976, 163752, 192976, 225942, 262956, 304336, 350412, 401526, 458032, 520296, 588696, 663622, 745476, 834672, 931636, 1036806

Offset: 1

Author

Vaclav Kotesovec, Jan 26 2010

Keywords

• easy
• nonn

Comments

Zebra is a (fairy chess) leaper [2,3].

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Vaclav 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, A172123, A172132.

Programs

Magma

[n eq 1 select 0 else (n^4 -9*n^2 +40*n -48)/2: n in [1..50]]; // G. C. Greubel, Apr 19 2022

Mathematica

CoefficientList[Series[2x(3+3*x-4*x^2+8*x^3-4*x^4)/(1-x)^55, {x, 0, 40}], x] (* Vincenzo Librandi, May 26 2013 *)

SageMath

[(n^4 -9*n^2 +40*n -48 +16*bool(n==1))/2 for n in (1..50)] # G. C. Greubel, Apr 19 2022

Formula

a(n) = (n^4 - 9*n^2 + 40*n - 48)/2, n >= 2. (Christian Poisson, 1990)

G.f.: 2*x^2*(3+3*x-4*x^2+8*x^3-4*x^4)/(1-x)^5. - Vaclav Kotesovec, Mar 25 2010

E.g.f.: (1/2)*(16*(3+x) + (-48 + 32*x - 2*x^2 + 6*x^3 + x^4)*exp(x)). - G. C. Greubel, Apr 19 2022