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A172965 Number of ways to place 3 nonattacking knights on an n X n cylindrical board. 3
0, 0, 6, 240, 1010, 4056, 12068, 30000, 65628, 130480, 240856, 418968, 694200, 1104488, 1697820, 2533856, 3685668, 5241600, 7307248, 10007560, 13489056, 17922168, 23503700, 30459408, 39046700, 49557456, 62320968, 77707000, 96128968, 118047240, 143972556 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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) = n*(n - 3)(n^4 + 3*n^3 - 18*n^2 - 18*n + 164)/6, n>=6.

G.f.: -2*x^3*(15*x^9-141*x^8+564*x^7-1276*x^6+1812*x^5-1652*x^4+908*x^3-272*x^2+99*x+3)/(x-1)^7. - Vaclav Kotesovec, Mar 25 2010

MATHEMATICA

CoefficientList[Series[- 2 x^2 (15 x^9 - 141 x^8 + 564 x^7 - 1276 x^6 + 1812 x^5 - 1652 x^4 + 908 x^3 - 272 x^2 + 99 x + 3) / (x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, May 29 2013 *)

CROSSREFS

Cf. A172530, A172134, A172964.

Sequence in context: A256275 A235346 A077231 * A002022 A065948 A052510

Adjacent sequences:  A172962 A172963 A172964 * A172966 A172967 A172968

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Feb 06 2010

EXTENSIONS

More terms from Vincenzo Librandi, May 29 2013

STATUS

approved

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)