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 A190401 Number of ways to place 6 nonattacking grasshoppers on a toroidal chessboard of size n x n. 2
 0, 0, 0, 384, 19100, 557808, 5841780, 41338400, 209264796, 859752800, 2982181004, 9131392296, 25196132260, 63968987264, 151223202900, 336724832384, 711538908572, 1437022315440, 2787781494732, 5219454908200, 9464698212228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The Grasshopper moves on the same lines as a queen, but must jump over a hurdle to land on the square immediately beyond. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights (in English and Czech) FORMULA Explicit formula: a(n) = 1/720*n^2*(n^10 -15n^8 -480n^7 +2245n^6 + 2400n^5 +27255n^4 -342480n^3 +639934n^2 +471600n -865080) + 1/4*n^2*(-1)^n*(8n^4 -40n^3 +17n^2 -272n +1608), n>8. G.f.: -4x^4*(128x^24 -768x^23 -8x^22 +9258x^21 -17442x^20 -25593x^19 +103542x^18 -19695x^17 -252858x^16 +225766x^15 +297416x^14 -465166x^13 -63474x^12 +488076x^11 +515008x^10 +582376x^9 +2358586x^8 +2976026x^7 +6280504x^6 +4731396x^5 +2785972x^4 +664045x^3 +111570x^2 +4199x +96)/((x-1)^13*(x+1)^7). MATHEMATICA CoefficientList[Series[- 4 x^3 (128 x^24 - 768 x^23 - 8 x^22 + 9258 x^21 - 17442 x^20 - 25593 x^19 + 103542 x^18 - 19695 x^17 - 252858 x^16 + 225766 x^15 + 297416 x^14 - 465166 x^13 - 63474 x^12 + 488076 x^11 + 515008 x^10 + 582376 x^9 + 2358586 x^8 + 2976026 x^7 + 6280504 x^6 + 4731396 x^5 + 2785972 x^4 + 664045 x^3 + 111570 x^2 + 4199 x + 96) / ((x - 1)^13 (x + 1)^7), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 03 2013 °) CROSSREFS Cf.: A190398, A190399, A190400. Sequence in context: A281656 A128967 A168675 * A256727 A023098 A188783 Adjacent sequences: A190398 A190399 A190400 * A190402 A190403 A190404 KEYWORD nonn,easy AUTHOR Vaclav Kotesovec, May 10 2011 STATUS approved

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Last modified December 8 14:17 EST 2022. Contains 358693 sequences. (Running on oeis4.)