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 A172201 Number of ways to place 3 nonattacking amazons (superqueens) on an n X n board. 5
 0, 0, 0, 0, 48, 424, 1976, 6616, 17852, 41544, 86660, 166288, 298616, 508200, 827168, 1296744, 1968676, 2907016, 4189772, 5910944, 8182400, 11136168, 14926536, 19732600, 25760588, 33246664, 42459476, 53703216, 67320392, 83695144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS An amazon (superqueen) moves like a queen and a knight. REFERENCES Panos Louridas, idee & form 93/2007, pp. 2936-2938. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Vaclav Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes Index entries for linear recurrences with constant coefficients, signature (5,-8,0,14,-14,0,8,-5,1). FORMULA Explicit formula (Panos Louridas, 2007): a(n) = (2*n^6 - 20*n^5 + 31*n^4 + 314*n^3 - 1452*n^2 + 2040*n - 672)/12 if n is even (n >= 4) and a(n) = (2*n^6 - 20*n^5 + 31*n^4 + 314*n^3 - 1452*n^2 + 2034*n - 669)/12 if n is odd (n >= 5). G.f.: 4*x^5*(12+46*x+60*x^2+32*x^3-23*x^4-13*x^5+7*x^6-x^7)/((1+x)^2*(1-x)^7). - Vaclav Kotesovec, Mar 24 2010 a(n) = (1/24)*(4*n^6 - 40*n^5 + 62*n^4 + 628*n^3 - 2904*n^2 + 4074*n - 1341 + 3*(-1)^n*(2*n-1)) - 20*[n=1] - 8*[n=2] + 4*[n=3]. - G. C. Greubel, Apr 29 2022 MATHEMATICA CoefficientList[Series[4*x^5*(12+46*x+60*x^2+32*x^3-23*x^4-13*x^5+7*x^6-x^7)/((1+x)^2*(1-x)^7), {x, 0, 40}], x] (* Vincenzo Librandi, May 27 2013 *) PROG (Magma) R:=PowerSeriesRing(Integers(), 40); [0, 0, 0, 0] cat Coefficients(R!( 4*x^5*(12+46*x+60*x^2+32*x^3-23*x^4-13*x^5+7*x^6-x^7)/((1+x)^2*(1-x)^7 ))); // G. C. Greubel, Apr 29 2022 (SageMath) [(1/24)*(4*n^6 -40*n^5 +62*n^4 +628*n^3 -2904*n^2 +4074*n -1341 +3*(-1)^n*(2*n-1)) -4*(5*bool(n==1) +2*bool(n==2) -bool(n==3)) for n in (1..40)] # G. C. Greubel, Apr 29 2022 CROSSREFS Cf. A047659, A051223, A051224, A061989, A172200. Sequence in context: A019558 A339761 A232917 * A249293 A347168 A281374 Adjacent sequences: A172198 A172199 A172200 * A172202 A172203 A172204 KEYWORD nonn,easy AUTHOR Vaclav Kotesovec, Jan 29 2010 STATUS approved

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Last modified June 20 23:53 EDT 2024. Contains 373535 sequences. (Running on oeis4.)