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A172214 Number of ways to place 5 nonattacking knights on a 5 X n board. 5
1, 28, 259, 1968, 9386, 30842, 82738, 192336, 400277, 763984, 1360797, 2291056, 3681226, 5687022, 8496534, 12333352, 17459691, 24179516, 32841667, 43842984, 57631432, 74709226, 95635956, 121031712, 151580209 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = (625n^5-8250n^4+57235n^3-242778n^2+608440n-705984)/24, n>=8.

G.f.: x * (42*x^12 -52*x^11 -268*x^10 +884*x^9 -268*x^8 -1188*x^7 +2834*x^6 -720*x^5 +918*x^4 +814*x^3 +106*x^2 +22*x +1) / (x-1)^6. - Vaclav Kotesovec, Mar 25 2010

MATHEMATICA

CoefficientList[Series[(42 x^12 - 52 x^11 - 268 x^10 + 884 x^9 - 268 x^8 - 1188 x^7 + 2834 x^6 - 720 x^5 + 918 x^4 + 814 x^3 + 106 x^2 + 22 x + 1) / (x - 1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 27 2013 *)

CROSSREFS

Cf. A172136, A061991, A172212, A172213.

Sequence in context: A240003 A225242 A189606 * A093196 A179098 A223111

Adjacent sequences:  A172211 A172212 A172213 * A172215 A172216 A172217

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jan 29 2010

STATUS

approved

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Last modified December 18 21:01 EST 2018. Contains 318245 sequences. (Running on oeis4.)