A152135 Maximal length of rook tour on an n X n+4 board.

12, 36, 74, 134, 216, 328, 470, 650, 868, 1132, 1442, 1806, 2224, 2704, 3246, 3858, 4540, 5300, 6138, 7062, 8072, 9176, 10374, 11674, 13076, 14588, 16210, 17950, 19808, 21792, 23902, 26146, 28524, 31044, 33706, 36518, 39480, 42600, 45878

Offset: 1

Author

R. J. Mathar, Mar 22 2009

Keywords

• nonn
• easy

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

Cf. A006071, A152132, A152133, A152134.

Programs

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

Mathematica

LinearRecurrence[{3, -2, -2, 3, -1}, {12, 36, 74, 134, 216}, 40] (* Vincenzo Librandi, Dec 11 2012 *)

Formula

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

From R. J. Mathar, May 13 2010: (Start)

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

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