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A172220 Number of ways to place 5 nonattacking nightriders on a 5 X n board. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A061991, A172214, A172218, A172219.

Sequence in context: A002593 A015881 A026910 * A255151 A184607 A215699

Adjacent sequences:  A172217 A172218 A172219 * A172221 A172222 A172223

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 29 2010

STATUS

approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)