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A108792
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Number of ways to place 5 nonattacking queens on an n X n board.
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11
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10, 248, 4618, 46736, 310496, 1535440, 6110256, 20609544, 60963094, 162323448, 396155466, 899046952, 1917743448, 3879011584, 7491080844, 13892164232, 24854703014, 43071383040, 72532831794, 119038462248, 190849299076
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OFFSET
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5,1
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LINKS
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Table of n, a(n) for n=5..25.
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FORMULA
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Explicit formula (Vaclav Kotesovec, 4.4.2010): a(n) = 1/120*n^10-5/18*n^9+301/72*n^8-1679/45*n^7+78383/360*n^6-77519/90*n^5+1867681/810*n^4-6499681/1620*n^3+5324093/1296*n^2-12758453/6480*n+13038851/64800+(1/8*n^5-143/48*n^4+82/3*n^3-5647/48*n^2+10475/48*n-3547/32)*(-1)^n+(29/2*n-35/2)*cos(pi*n/2)+(2*n+15)*sin(pi*n/2)+(+32/27*n^3-1328/81*n^2+6328/81*n-5488/81)*cos(2*pi*n/3)+(40*sqrt(3)/81*n^2-1496*sqrt(3)/243*n+7024*sqrt(3)/243)*sin(2*pi*n/3)+((8*sqrt(5)/25+8/5)*n-16*sqrt(5)/25-64/25)*cos(2*pi*n/5)+8*sqrt(22*sqrt(5)+50)/25*sin(2*pi*n/5)+((8/5-8*sqrt(5)/25)*n+16*sqrt(5)/25-64/25)*cos(pi*n/5)*(-1)^n-8*sqrt(50-22*sqrt(5))/25*sin(pi*n/5)*(-1)^n [From Vaclav Kotesovec, Apr 04 2010]
G.f.: -x^5*(14206*x^31+150238*x^30+916976*x^29+3972232*x^28+13522008*x^27+37968860*x^26+90996604*x^25+190236360*x^24+352607230*x^23+586165718*x^22+881664746*x^21+1207443842*x^20+1512654886*x^19+1738866194*x^18+1837742548*x^17+1786911600*x^16+1598078300*x^15+1312598856*x^14+987611934*x^13+677994354*x^12+422347390*x^11+236939238*x^10+118533110*x^9+52176470*x^8+19855936*x^7+6376140*x^6+1672768*x^5+341612*x^4+50540*x^3+4836*x^2+258*x+10)/((x-1)^11*(x+1)^6*(x^2+1)^2*(x^2+x+1)^4*(x^4+x^3+x^2+x+1)^2),
Recurrence: a(n)= - a(n-1) + 3*a(n-2) + 7*a(n-3) + 3*a(n-4) - 11*a(n-5) - 21*a(n-6) - 13*a(n-7) + 13*a(n-8) + 41*a(n-9) + 44*a(n-10) + 8*a(n-11) - 49*a(n-12) - 81*a(n-13) - 57*a(n-14) + 15*a(n-15) + 88*a(n-16) +106*a(n-17) + 48*a(n-18) - 48*a(n-19) -106*a(n-20) - 88*a(n-21) - 15*a(n-22) + 57*a(n-23) + 81*a(n-24) + 49*a(n-25) - 8*a(n-26) - 44*a(n-27) - 41*a(n-28) - 13*a(n-29) + 13*a(n-30) + 21*a(n-31) + 11*a(n-32) - 3*a(n-33) - 7*a(n-34) - 3*a(n-35) + a(n-36) + a(n-37) [From Vaclav Kotesovec, Apr 05 2010]
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CROSSREFS
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Cf. A047659, A061994.
Sequence in context: A034222 A197437 A211093 * A128013 A178021 A134262
Adjacent sequences: A108789 A108790 A108791 * A108793 A108794 A108795
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KEYWORD
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nonn
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AUTHOR
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Sergey Perepechko, Jul 09 2005
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STATUS
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approved
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