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A172215 Number of ways to place 6 nonattacking knights on a 6 X n board.

%I A172215 #20 Apr 16 2023 21:28:33
%S A172215 1,58,729,8830,60285,257318,858262,2404448,5879329,12927182,26115008,
%T A172215 49238436,87675623,148787822,242366502,381127124,581249573,862965246,
%U A172215 1251190796,1776208532,2474393475,3388987070,4570917554,6079666980
%N A172215 Number of ways to place 6 nonattacking knights on a 6 X n board.
%H A172215 Vincenzo Librandi, <a href="/A172215/b172215.txt">Table of n, a(n) for n = 1..1000</a>
%H A172215 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>
%H A172215 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7, -21, 35, -35, 21, -7, 1).
%F A172215 a(n) = (648n^6-11340n^5+103770n^4-606645n^3+2328317n^2-5466660n+6051720)/10, n>=10.
%F A172215 G.f.: -x * (104*x^15 -116*x^14 -1328*x^13 +3992*x^12 +806*x^11 -16380*x^10 +27343*x^9 -4845*x^8 -15537*x^7 +38275*x^6 -2753*x^5 +11789*x^4 +4910*x^3 +344*x^2 +51*x +1) / (x-1)^7. - _Vaclav Kotesovec_, Mar 25 2010
%F A172215 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - _Wesley Ivan Hurt_, Apr 16 2023
%t A172215 CoefficientList[Series[-(104 x^15 - 116 x^14 - 1328 x^13 + 3992 x^12 + 806 x^11 - 16380 x^10 + 27343 x^9 - 4845 x^8 - 15537 x^7 + 38275 x^6 - 2753 x^5 + 11789 x^4 + 4910 x^3 + 344 x^2 + 51 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%t A172215 LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,58,729,8830,60285,257318,858262,2404448,5879329,12927182,26115008,49238436,87675623,148787822,242366502,381127124},30] (* _Harvey P. Dale_, Dec 31 2022 *)
%Y A172215 Cf. A061992, A172212, A172213, A172214.
%K A172215 nonn,easy
%O A172215 1,2
%A A172215 _Vaclav Kotesovec_, Jan 29 2010