A195661 - OEIS

%I #13 Aug 28 2024 13:18:27

%S 8192,1270246,44653028,720390254,7177627944,51526819510,291859775552,

%T 1382652697282,5700499630916,21042965606234,71028444904044,

%U 222770819826574,657397551407816,1843639061043694,4953451546255928,12835026767559890,32249277650536068

%N Number of ways to place 12n nonattacking kings on a vertical cylinder 24 X 2n.

%C Vertical cylinder: a chessboard where it is supposed that the columns 1 and 24 are in contact (number of columns = 24, number of rows = 2n).

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (15, -103, 429, -1210, 2442, -3630, 4026, -3333, 2035, -891, 265, -48, 4).

%F Recurrence: a(n) = 4*a(n-13) - 48*a(n-12) + 265*a(n-11) - 891*a(n-10) + 2035*a(n-9) - 3333*a(n-8) + 4026*a(n-7) - 3630*a(n-6) + 2442*a(n-5) - 1210*a(n-4) + 429*a(n-3) - 103*a(n-2) + 15*a(n-1).

%F G.f.: -(1 + 8177*x + 1147469*x^2 + 26442685*x^3 + 177917014*x^4 + 436010362*x^5 + 423443926*x^6 + 163698250*x^7 + 23613841*x^8 + 1078869*x^9 + 9965*x^10 + 41*x^11)/((x-1)^11*(2*x-1)^2).

%F a(n) = (74405871551*n - 1097352668753)*2^n + 696317/2016*n^10 + 420699809/30240*n^9 + 66463031/210*n^8 + 26602370087/5040*n^7 + 33515235289/480*n^6 + 1076425504013/1440*n^5 + 32380230257101/5040*n^4 + 325331895133417/7560*n^3 + 29685456992323/140*n^2 + 72053208873316/105*n + 1097352668754.

%Y Cf. A195656, A195651, A137432.

%K nonn

%O 1,1

%A _Vaclav Kotesovec_, Sep 22 2011