A187241 Number of ways to place 9 nonattacking bishops on an n X n board.

0, 0, 0, 0, 0, 1600, 389312, 22057472, 565532992, 8611750848, 90564534336, 720227187456, 4603893554496, 24675964279680, 114402835995392, 469601097840640, 1737913582100864, 5882030372643968, 18417596366384512, 53854324059153920, 148209412582029184, 386390343290393024, 959556901097413696

Offset

1,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks), arXiv preprint arXiv:1609.00853, a12016

V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech)

Formula

a(n) = n^18/362880 - n^17/7560 + 181n^16/60480 - 14509n^15/340200 + 2101n^14/4860 - 101071n^13/30240 + 112406401n^12/5443200 - 143351879n^11/1360800 + 2465350549n^10/5443200 - 14081834n^9/8505 + 55888723201n^8/10886400 - 6055816813n^7/453600 + 155816526107n^6/5443200 - 13489156949n^5/272160 + 183801705823n^4/2721600 - 15816472541n^3/226800 + 30820237351n^2/604800 - 919392091n/40320 + 1101239/256 + (-n^12/5760 + 11n^11/1440 - 113n^10/720 + 51793n^9/25920 - 202873n^8/11520 + 3428791n^7/30240 - 1050169n^6/1920 + 8590259n^5/4320 - 1034689n^4/192 + 68481311n^3/6480 - 81534479n^2/5760 + 465686363n/40320 - 1101239/256)*(-1)^n.

G.f.: -64x^6*(5670x^25 + 116100x^24 + 2282283x^23 + 25883910x^22 + 220244661x^21 + 1330673229x^20 + 6121839129x^19 + 21511823232x^18 + 59645434477x^17 + 131494649245x^16 + 234424379246x^15 + 339339084372x^14 + 401937236082x^13 + 389328811002x^12 + 308645316626x^11 + 199052247464x^10 + 103780570480x^9 + 43151321222x^8 + 14078209111x^7 + 3508317590x^6 + 644755881x^5 + 82579449x^4 + 6782181x^3 + 308200x^2 + 5933x + 25)/((x-1)^19*(x+1)^13).

a(9) = A002465(9).

Mathematica

CoefficientList[Series[- 64 x^5 (5670 x^25 + 116100 x^24 + 2282283 x^23 + 25883910 x^22 + 220244661 x^21 + 1330673229 x^20 + 6121839129 x^19 + 21511823232 x^18 + 59645434477 x^17 + 131494649245 x^16 + 234424379246 x^15 + 339339084372 x^14 + 401937236082 x^13 + 389328811002 x^12 + 308645316626 x^11 + 199052247464 x^10 + 103780570480 x^9 + 43151321222 x^8 + 14078209111 x^7 + 3508317590 x^6 + 644755881 x^5 + 82579449 x^4 + 6782181 x^3 + 308200 x^2 + 5933 x + 25) / ((x - 1)^19 (x + 1)^13), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 02 2013 *)

Crossrefs

Cf. A172123, A172124, A172127, A172129, A176886, A187239, A187240.

Sequence in context: A236992 A251969 A206250 * A323496 A279241 A060566

Adjacent sequences: A187238 A187239 A187240 * A187242 A187243 A187244

Keyword

nonn,easy

Author

Vaclav Kotesovec, Mar 07 2011

Status

approved