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A172137
Number of ways to place 2 nonattacking zebras on an n X n board.
7
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
1,2
COMMENTS
Zebra is a (fairy chess) leaper [2,3].
REFERENCES
Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p. 829.
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
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 *)
PROG
(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
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vaclav Kotesovec, Jan 26 2010
STATUS
approved