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A172124 Number of ways to place 3 nonattacking bishops on an n X n board. 15
0, 0, 26, 232, 1124, 3896, 10894, 26192, 56296, 110960, 204130, 355000, 589196, 940072, 1450134, 2172576, 3172944, 4530912, 6342186, 8720520, 11799860, 15736600, 20711966, 26934512, 34642744, 44107856, 55636594, 69574232 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

E. Bonsdorff, K. Fabel, O. Riihimaa, Schach und Zahl, 1966, p. 51-63

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

FORMULA

Explicit formulas (Karl Fabel, 1966): a(n) = n(n - 2)(2n^4 - 4n^3 + 7n^2 - 6n + 4)/12 if n is even, and a(n) = (n - 1)(2n^5 - 6n^4 + 9n^3 - 11n^2 + 5n - 3)/12 if n is odd.

G.f.: -2*x^3*(3*x^4+18*x^3+48*x^2+38*x+13)/((x-1)^7*(x+1)). [.Vaclav Kotesovec, Mar 25 2010]

a(n) = (2*(n-2)*n*(2*n^4-4*n^3+7*n^2-6*n+4)-3*(-1)^n+3)/24. [Bruno Berselli, May 26 2013]

MATHEMATICA

CoefficientList[Series[-2 x^2 (3 x^4 + 18 x^3 + 48 x^2 + 38 x + 13) / ((x-1)^7 (x+1)), {x, 0, 30}], x] (* Vincenzo Librandi, May 26 2013 *)

CROSSREFS

Cf. A047659, A172123.

Sequence in context: A159519 A110486 A098994 * A196633 A196638 A163726

Adjacent sequences:  A172121 A172122 A172123 * A172125 A172126 A172127

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 26 2010

STATUS

approved

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Last modified November 28 04:44 EST 2014. Contains 250286 sequences.