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A243717 Number of inequivalent (mod D_4) ways to place 2 nonattacking knights on an n X n board. 5
2, 7, 18, 43, 83, 156, 257, 418, 624, 925, 1292, 1797, 2393, 3178, 4083, 5236, 6542, 8163, 9974, 12175, 14607, 17512, 20693, 24438, 28508, 33241, 38352, 44233, 50549, 57750, 65447, 74152, 83418, 93823, 104858, 117171, 130187, 144628, 159849, 176650, 194312 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Rotations or reflections of a placement are considered as the same. If they are distinguished, numbers are A172132.

LINKS

Heinrich Ludwig, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

FORMULA

a(n) = (n^4 - 2*n^2 + 20*n - 16 + IF(MOD(n, 2) = 1)*(2*n^2 - 4*n - 1))/16.

a(n) = (-33+(-1)^n+4*(9+(-1)^n)*n-2*(1+(-1)^n)*n^2+2*n^4)/32. - Colin Barker, Jun 10 2014

G.f.: x^2*(x^6-3*x^4-5*x^3-3*x-2) / ((x-1)^5*(x+1)^3). - Colin Barker, Jun 10 2014

MAPLE

A243717:=n->(-33+(-1)^n+4*(9+(-1)^n)*n-2*(1+(-1)^n)*n^2+2*n^4)/32; seq(A243717(n), n=2..50); # Wesley Ivan Hurt, Jun 11 2014

MATHEMATICA

Table[(-33 + (-1)^n + 4*(9 + (-1)^n)*n - 2*(1 + (-1)^n)*n^2 + 2*n^4)/

32, {n, 2, 50}] (* Wesley Ivan Hurt, Jun 11 2014 *)

PROG

(PARI) Vec(x^2*(x^6-3*x^4-5*x^3-3*x-2)/((x-1)^5*(x+1)^3) + O(x^100)) \\ Colin Barker, Jun 10 2014

(MAGMA) [ (-33+(-1)^n+4*(9+(-1)^n)*n-2*(1+(-1)^n)*n^2+2*n^4)/32: n in [2..50]]; // Wesley Ivan Hurt, Jun 11 2014

CROSSREFS

Cf. A243716, A172132, A243718, A243719, A243720.

Sequence in context: A007991 A037294 A076857 * A174192 A247289 A161870

Adjacent sequences:  A243714 A243715 A243716 * A243718 A243719 A243720

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Jun 10 2014

STATUS

approved

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Last modified November 21 22:16 EST 2019. Contains 329383 sequences. (Running on oeis4.)