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A172964 Number of ways to place 2 nonattacking knights on an n X n cylindrical board. 5
0, 4, 18, 92, 230, 522, 1022, 1808, 2970, 4610, 6842, 9792, 13598, 18410, 24390, 31712, 40562, 51138, 63650, 78320, 95382, 115082, 137678, 163440, 192650, 225602, 262602, 303968, 350030, 401130, 457622, 519872, 588258, 663170, 745010, 834192, 931142, 1036298, 1150110 (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) = n*(n^3 - 9*n + 12)/2, n>=5.

G.f.: 2*x^2*(6*x^7-30*x^6+61*x^5-66*x^4+45*x^3-21*x^2+x-2)/(x-1)^5. - Vaclav Kotesovec, Mar 25 2010

MATHEMATICA

CoefficientList[Series[2 x (6 x^7 - 30 x^6 + 61 x^5 - 66 x^4 + 45 * x^3 - 21 x^2 + x - 2) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 29 2013 *)

CROSSREFS

Cf. A172529, A172132.

Sequence in context: A355247 A269450 A206639 * A317135 A196150 A185298

Adjacent sequences: A172961 A172962 A172963 * A172965 A172966 A172967

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 November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)