A172218 -id:A172218 - cp's OEIS frontend

A172219 Number of ways to place 4 nonattacking nightriders on a 4 X n board.

1, 16, 84, 412, 1126, 2760, 5739, 10982, 19695, 33068, 52801, 80638, 118731, 169368, 235135, 318890, 423733, 553028, 710389, 899690, 1125059, 1390880, 1701793, 2062694, 2478735, 2955324, 3498125, 4113058, 4806299, 5584280, 6453689

Offset: 1

Vaclav Kotesovec, Jan 29 2010

A nightrider is a fairy chess piece that can move (proportionate to how a knight moves) in any direction.

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

Cf. A061990, A172213, A172218.

CoefficientList[Series[-(2 x^21 - 6 x^20 + 10 x^19 - 14 x^18 + 22 x^17 - 30 x^16 - 26 x^15 + 162 x^14 - 272 x^13 + 364 x^12 - 466 x^11 + 526 x^10 - 303 x^9 - 207 x^8 + 603 x^7 - 517 x^6 + 489 x^5 - 249 x^4 + 142 x^3 + 14 x^2 + 11 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

a(n) = (32n^4 - 432n^3 + 3190n^2 - 13323n + 25530)/3, n>=18.

G.f.: -x * (2*x^21 -6*x^20 +10*x^19 -14*x^18 +22*x^17 -30*x^16 -26*x^15 +162*x^14 -272*x^13 +364*x^12 -466*x^11 +526*x^10 -303*x^9 -207*x^8 +603*x^7 -517*x^6 +489*x^5 -249*x^4 +142*x^3 +14*x^2 +11*x +1) / (x-1)^5. - Vaclav Kotesovec, Mar 25 2010

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

Vaclav Kotesovec, Jan 29 2010

A nightrider is a fairy chess piece that can move (proportionate to how a knight moves) in any direction.

Vaclav Kotesovec and Vincenzo Librandi, Table of n, a(n) for n = 1..1000 (first 40 terms from V. Kotesovec)
V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Cf. A061991, A172214, A172218, A172219.

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 *)

a(n) = (625n^5-15250n^4+197915n^3-1588634n^2+7645896n-17283552)/24, n>=32.

G.f.: x * (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. - Vaclav Kotesovec, Mar 25 2010

cp's OEIS Frontend

A172219 Number of ways to place 4 nonattacking nightriders on a 4 X n board.

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