A172138 Number of ways to place 3 nonattacking zebras on an n X n board.

0, 4, 84, 452, 1772, 5596, 14888, 34640, 72712, 140716, 255036, 437968, 718980, 1136092, 1737376, 2582576, 3744848, 5312620, 7391572, 10106736, 13604716, 18056028, 23657560, 30635152, 39246296, 49782956, 62574508, 77990800

Offset: 1

Author

Vaclav Kotesovec, Jan 26 2010

Keywords

• nonn
• easy

Comments

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

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 (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A047659, A172124, A172134, A172137.

Programs

Magma

[0,4,84,452,1772] cat [(n^6 -27*n^4 +120*n^3 +74*n^2 -1608*n +2976)/6: n in [6..50]]; // G. C. Greubel, Apr 19 2022

Mathematica

CoefficientList[Series[4x(1+14*x-13*x^2+58*x^3-29*x^4-9*x^5+x^6+ 33*x^7- 45*x^8 +23*x^9-4*x^10)/(1-x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,4,84,452,1772,5596,14888,34640,72712,140716,255036,437968},30] (* Harvey P. Dale, Mar 11 2023 *)

SageMath

[0,4,84,452,1772]+[(n^6 -27*n^4 +120*n^3 +74*n^2 -1608*n +2976)/6 for n in (6..50)] # G. C. Greubel, Apr 19 2022

Formula

a(n) = (n^6 - 27*n^4 + 120*n^3 + 74*n^2 - 1608*n + 2976)/6, n >=6.

G.f.: 4*x^2*(1 + 14*x - 13*x^2 + 58*x^3 - 29*x^4 - 9*x^5 + x^6 + 33*x^7 - 45*x^8 + 23*x^9 - 4*x^10)/(1-x)^7. - Vaclav Kotesovec, Mar 25 2010