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A173783
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Number of ways to place 5n nonattacking kings on a 10 X 2n chessboard.
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8
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192, 7698, 166368, 2580754, 32572756, 357365350, 3544192112, 32580145116, 282359109140, 2335042206624, 18589546217696, 143422674213726, 1077891352444220, 7923134615854816, 57146364209686016, 405497952834408698
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: 2*x*(292626432*x^30 -7695378432*x^29 +94084706304*x^28 -712519981056*x^27 +3757888797696*x^26 -14715718076160*x^25 +44556058968960*x^24 -107273952716256*x^23 +209645023363168*x^22 -337824014576768*x^21 +454329405135504*x^20 -514643686425920*x^19 +494203416082160*x^18 -403847150294172*x^17 +281135354205764*x^16 -166453721883480*x^15 +83456844800670*x^14 -35182845104124*x^13 +12345883162136*x^12 -3557728594620*x^11 +827346101101*x^10 -152042822189*x^9 +21726065190*x^8 -2499103126*x^7 +289877178*x^6 -45817212*x^5 +7810422*x^4 -1012942*x^3 +86355*x^2 -4311*x+96) / ((1-2*x) *(x^2-4*x+1) *(4*x-1) *(6*x-1)^2 *(2*x^2-4*x+1) *(2*x^2-5*x+1) *(4*x^2-6*x+1)^2 *(6*x^2-6*x+1)^2 *(7*x^2-6*x+1)^2 *(2*x^3-8*x^2+6*x-1) *(3*x^3-9*x^2+6*x-1)^2).
Recurrence: a(n) = 85a(n-1) -3441a(n-2) +88303a(n-3) -1613002a(n-4) +22327010a(n-5) -243429637a(n-6) +2145452227a(n-7) -15565947848a(n-8) +94202823084a(n-9) -480152808502a(n-10) +2075863416838a(n-11) -7651361422835a(n-12) +24128330540449a(n-13) -65240466585284a(n-14) +151411770874148a(n-15) -301613628545814a(n-16) +515173613407544a(n-17) -753006145475828a(n-18) +939001403456656a(n-19) -994821988961592a(n-20) +890558910282768a(n-21) -668920434927504a(n-22) +417832289937792a(n-23) -214574645977920a(n-24) +89258591798784a(n-25) -29486236792320a(n-26) +7526493775872a(n-27) -1426182018048a(n-28) +188221833216a(n-29) -15390756864a(n-30) +585252864a(n-31), n>31.
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MATHEMATICA
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CoefficientList[Series[2 (292626432 x^30 - 7695378432 x^29 + 94084706304 x^28 - 712519981056 x^27 + 3757888797696 x^26 - 14715718076160 x^25 + 44556058968960 x^24 - 107273952716256 x^23 + 209645023363168 x^22 - 337824014576768 x^21 + 454329405135504 x^20 - 514643686425920 x^19 + 494203416082160 x^18 - 403847150294172 x^17 + 281135354205764 x^16 - 166453721883480 x^15 + 83456844800670 x^14 - 35182845104124 x^13 + 12345883162136 x^12 - 3557728594620 x^11 + 827346101101 x^10 - 152042822189 x^9 + 21726065190 x^8 - 2499103126 x^7 + 289877178 x^6 - 45817212 x^5 + 7810422 x^4 - 1012942 x^3 + 86355 x^2 - 4311 x + 96) / ((1 - 2 x) (x^2 - 4 x + 1) (4 x - 1) (6 x - 1)^2 (2 x^2 - 4 x + 1) (2 x^2 - 5 x + 1) (4 x^2 - 6 x + 1)^2 (6 x^2 - 6 x + 1)^2 (7 x^2 - 6 x + 1)^2 (2 x^3 - 8 x^2 + 6 x - 1) (3 x^3 - 9 x^2 + 6 x - 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, May 30 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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