A172227
Number of ways to place 4 nonattacking wazirs on an n X n board.
Original entry on oeis.org
0, 0, 6, 405, 5024, 31320, 133544, 446421, 1258590, 3126724, 7042930, 14669709, 28658436, 53069000, 93909924, 159819965, 262913874, 419816676, 652912510, 991835749, 1475233800, 2152832664, 3087838016, 4359706245, 6067321574, 8332617060, 11304678954
Offset: 1
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- J. Brazeal Slides on a Chessboard, Math Horizons, Vol. 27, pp. 24-27, April 2020.
- Vaclav Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
- Eric Weisstein's World of Mathematics, Grid Graph
- Wikipedia, Fairy chess piece
- Wikipedia, Wazir (chess)
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CoefficientList[Series[- x^2 (4 x^8 - 26 x^7 + 3 x^6 + 303 x^5 - 736 x^4 + 180 x^3 + 1595 x^2 + 351 x + 6) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)
A172140
Number of ways to place 5 nonattacking zebras on an n X n board.
Original entry on oeis.org
0, 0, 126, 2032, 20502, 160696, 929880, 4117520, 15037036, 47368960, 132577826, 336828368, 789558314, 1729320120, 3574328936, 7027309888, 13226773092, 23959787480, 41954706558, 71276149776, 117848892710, 190142197976
Offset: 1
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Vaclav 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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).
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CoefficientList[Series[2x^2(100x^19 -648x^18 +1450x^17 -2126x^16 +10452x^15 - 43872x^14 +92798x^13 -100834x^12 +56460x^11 -61636x^10 +182288x^9 -303224x^8 + 275038x^7 -128982x^6 +21681x^5 +1933x^4 -13072x^3 -2540x^2 -323x-63)/(x-1)^11, {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *)
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[0,0,126,2032,20502,160696,929880,4117520,15037036,47368960,132577826] + [(n^10 -90*n^8 +400*n^7 +2915*n^6 -26880*n^5 +2430*n^4 +609920*n^3 - 1517496*n^2 -4188480*n +16581120)/120 for n in (12..50)] # G. C. Greubel, Apr 19 2022
A244284
Number of ways to place n nonattacking zebras on an n X n chessboard.
Original entry on oeis.org
1, 6, 84, 1168, 20502, 525796, 18939708, 802444170, 38934305898, 2170312156170
Offset: 1
A172222
Number of ways to place 4 nonattacking zebras on a 4 X n board.
Original entry on oeis.org
1, 70, 406, 1168, 2948, 6576, 13122, 23808, 40168, 63996, 97344, 142516, 202072, 278828, 375856, 496484, 644296, 823132, 1037088, 1290516, 1588024, 1934476, 2334992, 2794948, 3319976
Offset: 1
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CoefficientList[Series[-(4 x^12 - 6 x^11 - 2 x^10 - 52 x^9 + 160 x^8 - 88 x^7 + 2 x^6 - 195 x^5 + 473 x^4 - 172 x^3 + 66 x^2 + 65 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)
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