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A242358 Number of inequivalent (mod D_4) ways five checkers can be placed on an n X n board. 4
23, 567, 6814, 47358, 239511, 954226, 3207212, 9414828, 24862239, 60136329, 135311658, 286229762, 574460495, 1101240084, 2028333848, 3605765688, 6211552455, 10402472811, 16984387958, 27099325638, 42342870823, 64905898662, 97761436356, 144885584740, 211543443215 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Heinrich Ludwig, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4,-20,40,16,-100,44,110,-110,-44,100,-16,-40,20,4,-5,1).

FORMULA

a(n) = (n^10 - 10*n^8 + 35*n^6 + 52*n^5 - 210*n^4 + 140*n^3 - 56*n^2 + 48*n + IF(MOD(n, 2) = 1)*(52*n^5 - 145*n^4 + 140*n^3 - 80*n^2 + 48*n - 15))/960.

G.f.: x^3*(-23 - 452*x - 4071*x^2 - 16016*x^3 - 40397*x^4 - 59335*x^5 - 61954*x^6 - 38236*x^7 - 17221*x^8 - 3614*x^9 - 623*x^10 + 20*x^11 + x^12 + x^13)/((x-1)^11*(x+1)^6). - Vaclav Kotesovec, May 11 2014

a(n) = A054772(n, 5), n >=3. - Wolfdieter Lang, Oct 03 2016

MATHEMATICA

Drop[CoefficientList[Series[x^3*(-23 - 452*x - 4071*x^2 - 16016*x^3 - 40397*x^4 - 59335*x^5 - 61954*x^6 - 38236*x^7 - 17221*x^8 - 3614*x^9 - 623*x^10 + 20*x^11 + x^12 + x^13)/((x-1)^11*(x+1)^6), {x, 0, 20}], x], 3] (* Vaclav Kotesovec, May 11 2014 *)

CROSSREFS

Cf. A054252, A008805, A014409, A082966, A242279, A054772.

Sequence in context: A158631 A196536 A231261 * A043347 A015696 A106538

Adjacent sequences:  A242355 A242356 A242357 * A242359 A242360 A242361

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, May 11 2014

STATUS

approved

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Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)