A152135 - OEIS

%I #19 Apr 20 2023 04:23:43

%S 12,36,74,134,216,328,470,650,868,1132,1442,1806,2224,2704,3246,3858,

%T 4540,5300,6138,7062,8072,9176,10374,11674,13076,14588,16210,17950,

%U 19808,21792,23902,26146,28524,31044,33706,36518,39480,42600,45878

%N Maximal length of rook tour on an n X n+4 board.

%D M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 76.

%H Vincenzo Librandi, <a href="/A152135/b152135.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).

%F G.f.: -2*x*(-6+5*x^2-4*x^3+x^4)/(1+x)/(x-1)^4.

%F From _R. J. Mathar_, May 13 2010: (Start)

%F a(n) = +3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).

%F a(n) = 19*n/3+3/2+2*n^3/3+4*n^2+(-1)^n/2. (End)

%t LinearRecurrence[{3, -2, -2, 3, -1}, {12, 36, 74, 134, 216}, 40] (* _Vincenzo Librandi_, Dec 11 2012 *)

%o (Magma) I:=[12, 36, 74, 134, 216]; [n le 5 select I[n] else 3*Self(n-1)-2*Self(n-2)-2*Self(n-3)+3*Self(n-4)-Self(n-5): n in [1..40]]; // _Vincenzo Librandi_, Dec 11 2012

%Y Cf. A006071, A152132, A152133, A152134.

%K nonn,easy

%O 1,1

%A _R. J. Mathar_, Mar 22 2009