A172215
Number of ways to place 6 nonattacking knights on a 6 X n board.
Original entry on oeis.org
1, 58, 729, 8830, 60285, 257318, 858262, 2404448, 5879329, 12927182, 26115008, 49238436, 87675623, 148787822, 242366502, 381127124, 581249573, 862965246, 1251190796, 1776208532, 2474393475, 3388987070, 4570917554, 6079666980
Offset: 1
- 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
- Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
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CoefficientList[Series[-(104 x^15 - 116 x^14 - 1328 x^13 + 3992 x^12 + 806 x^11 - 16380 x^10 + 27343 x^9 - 4845 x^8 - 15537 x^7 + 38275 x^6 - 2753 x^5 + 11789 x^4 + 4910 x^3 + 344 x^2 + 51 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,58,729,8830,60285,257318,858262,2404448,5879329,12927182,26115008,49238436,87675623,148787822,242366502,381127124},30] (* Harvey P. Dale, Dec 31 2022 *)
A172217
Number of ways to place 7 nonattacking knights on a 7 X n board.
Original entry on oeis.org
1, 78, 1758, 38588, 383246, 2135344, 8891854, 30108310, 86669806, 219845764, 504261973, 1065642840, 2104251027, 3924818982, 6973786593, 11884673662, 19532410762, 31097451768, 48140491605, 72688612756, 107333684073
Offset: 1
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CoefficientList[Series[(252 x^18 - 272 x^17 - 5134 x^16 + 14468 x^15 + 19721 x^14 - 132666 x^13 + 174233 x^12 + 119440 x^11 - 540473 x^10 + 654954 x^9 - 89133 x^8 - 93778 x^7 + 497782 x^6 + 56796 x^5 + 119468 x^4 + 26652 x^3 + 1162 x^2 + 70 x + 1) / (x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)
A172220
Number of ways to place 5 nonattacking nightriders on a 5 X n board.
Original entry on oeis.org
1, 28, 157, 1248, 4650, 15162, 37988, 86958, 181423, 351708, 648441, 1127392, 1874194, 2988466, 4602096, 6870240, 9983347, 14163972, 19672403, 26812260, 35929480, 47418482, 61723238, 79341720, 100828175, 126796852, 157924785
Offset: 1
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CoefficientList[Series[(2 x^36 - 8 x^35 + 16 x^34 - 24 x^33 + 38 x^32 - 64 x^31 + 104 x^30 - 156 x^29 + 54 x^28 + 380 x^27 - 944 x^26 + 1452 x^25 - 2172 x^24 + 3376 x^23 - 5094 x^22 + 7180 x^21 - 6614 x^20 - 28 x^19 + 8814 x^18 - 15212 x^17 + 21026 x^16 - 27284 x^15 + 34160 x^14 - 40598 x^13 + 39882 x^12 - 24490 x^11 + 3876 x^10 + 8558 x^9 - 11326 x^8 + 11266 x^7 -6006 x^6 + 3256 x^5 - 1028 x^4 + 706 x^3 + 4 x^2 + 22 x + 1) / (x - 1)^6, {x, 0, 40}], x] (* Vincenzo Librandi, May 28 2013 *)
A174698
Number of ways to place 8 nonattacking knights on an 8 X n board.
Original entry on oeis.org
1, 81, 4409, 175720, 2479881, 17925691, 92952858, 379978716, 1286959255, 3765248749, 9805497200, 23226916560, 50866495373, 104288896551, 202154535834, 373400685738, 661407061211, 1129334088897, 1866838857216
Offset: 1
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CoefficientList[Series[(592 x^21 - 584 x^20 - 18100 x^19 + 49628 x^18 + 134264 x^17 - 735838 x^16 + 584418 x^15 + 2607764 x^14 - 7093608 x^13 + 5656936 x^12 + 5136811 x^11 - 13973779 x^10 + 14583702 x^9 - 1612610 x^8 + 2009820 x^7 + 6682287 x^6 + 1572406 x^5 + 1050447 x^4 + 138871 x^3 + 3716 x^2 + 72 x + 1) / (1 - x)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)
Showing 1-4 of 4 results.
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