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A172519 Number of ways to place 4 nonattacking queens on an n X n toroidal board. 7
0, 0, 0, 0, 50, 288, 2450, 16384, 62208, 233600, 638880, 1755072, 3901534, 8772176, 17051850, 33507328, 59175640, 105557904, 173570244, 287904000, 447885774, 702042000, 1044894554, 1565385984, 2247132500, 3244194304, 4519015596 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..27.

V. 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 (-1, 3, 6, 3, -9, -20, -11, 15, 40, 31, -15, -53, -50, 0, 50, 53, 15, -31, -40, -15, 11, 20, 9, -3, -6, -3, 1, 1).

FORMULA

a(n) = (n^8/24 - n^7 + 245n^6/24 - 113n^5/2 + 2843n^4/16 - 593n^3/2 + 4757n^2/24) + (n^6/8 - 5n^5/2 + 305n^4/16 - 129n^3/2 + 629n^2/8)*(-1)^n + 8n^2*cos(2*Pi*n/3)/3 + 9n^2*cos(Pi*n/2)/2.

Recurrence: a(n) = -a(n-1)+3a(n-2)+6a(n-3)+3a(n-4)-9a(n-5)-20a(n-6)-11a(n-7)+15a(n-8)+40a(n-9)+31a(n-10)-15a(n-11)-53a(n-12)-50a(n-13)+50a(n-15)+53a(n-16)+15a(n-17)-31a(n-18)-40a(n-19)-15a(n-20)+11a(n-21)+20a(n-22)+9a(n-23)-3a(n-24)-6a(n-25)-3a(n-26)+a(n-27)+a(n-28), n>=29. - Vaclav Kotesovec, Feb 09 2010

G.f.: -2*x^5*(287*x^22 +5191*x^21 +25616*x^20 +105043*x^19 +280800*x^18 +651461*x^17 +1186795*x^16 +1925172*x^15 +2611064*x^14 +3190574*x^13 +3337574*x^12 +3161250*x^11 +2574658*x^10 +1891298*x^9 +1175308*x^8 +649556*x^7 +291897*x^6 +115771*x^5 +34682*x^4 +8835*x^3 +1294*x^2 +169*x +25) / ((x -1)^9*(x +1)^7*(x^2 +1)^3*(x^2 +x +1)^3). - Colin Barker, Sep 21 2014

MATHEMATICA

LinearRecurrence[{-1, 3, 6, 3, -9, -20, -11, 15, 40, 31, -15, -53, -50, 0, 50, 53, 15, -31, -40, -15, 11, 20, 9, -3, -6, -3, 1, 1}, {0, 0, 0, 0, 0, 50, 288, 2450, 16384, 62208, 233600, 638880, 1755072, 3901534, 8772176, 17051850, 33507328, 59175640, 105557904, 173570244, 287904000, 447885774, 702042000, 1044894554, 1565385984, 2247132500, 3244194304, 4519015596}, 40] (* Harvey P. Dale, Apr 30 2018 *)

CROSSREFS

A061994, A007705, A172517, A172518.

Sequence in context: A186123 A220864 A205355 * A046656 A205620 A183698

Adjacent sequences:  A172516 A172517 A172518 * A172520 A172521 A172522

KEYWORD

nonn,nice

AUTHOR

Vaclav Kotesovec, Feb 05 2010

STATUS

approved

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)