A172139 Number of ways to place 4 nonattacking zebras on an n X n board.

0, 1, 126, 1168, 7334, 35749, 137970, 438984, 1208246, 2969389, 6662480, 13873100, 27144408, 50389581, 89424014, 152638280, 251834530, 403250693, 628798516, 957543164, 1427453780, 2087456085, 2999819778, 4242915176

Offset: 1

Author

Vaclav Kotesovec, Jan 26 2010

Keywords

• nonn

Comments

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 (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A061994, A172127, A172135, A172137, A172138.

Programs

Mathematica

CoefficientList[Series[x(1+117*x+70*x^2+1274*x^3+1333*x^4-2109*x^5-462*x^6 +8858*x^7-17006*x^8+15166*x^9-6838*x^10+1478*x^11-650*x^12+760*x^13-376*x^14 +64*x^15)/(1-x)^9, {x,0,40}], x] (* Vincenzo Librandi, May 27 2013 *)

SageMath

[0,1,126,1168,7334,35749,137970,438984] + [(n^8 -54*n^6 +240*n^5 +827*n^4 -8592*n^3 +10362*n^2 +75600*n -204864)/24 for n in (9..50)] # G. C. Greubel, Apr 19 2022

Formula

a(n) = (n^8 - 54*n^6 + 240*n^5 + 827*n^4 - 8592*n^3 + 10362*n^2 + 75600*n - 204864)/24, n >= 9.

G.f.: x^2*(1 + 117*x + 70*x^2 + 1274*x^3 + 1333*x^4 - 2109*x^5 - 462*x^6 + 8858*x^7 - 17006*x^8 + 15166*x^9 - 6838*x^10 + 1478*x^11 - 650*x^12 + 760*x^13 - 376*x^14 + 64*x^15)/(1-x)^9. - Vaclav Kotesovec, Mar 25 2010