A152134 Maximal length of rook tour on an n X n+3 board.

8, 24, 54, 102, 174, 270, 396, 556, 756, 996, 1282, 1618, 2010, 2458, 2968, 3544, 4192, 4912, 5710, 6590, 7558, 8614, 9764, 11012, 12364, 13820, 15386, 17066, 18866, 20786, 22832, 25008, 27320, 29768, 32358, 35094, 37982, 41022, 44220, 47580

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,-3,1,1,-3,3,-1).

Crossrefs

Cf. A006071, A152132, A152133, A152135.

Programs

Magma

I:=[8, 24, 54, 102, 174, 270, 396]; [n le 7 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3)+Self(n-4)-3*Self(n-5)+3*Self(n-6)-Self(n-7): n in [1..40]];// Vincenzo Librandi, Dec 19 2012

Mathematica

CoefficientList[Series[-2*(- 4 - 3*x^2 - 2*x^3 + x^4)/(1+x)/(x^2+1)/(x-1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2012 *)

Formula

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

a(n) = 17*n/6+3/4+2*n^3/3+3*n^2+A132429(n+3)/4. - R. J. Mathar, Sep 27 2009

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7). - Vincenzo Librandi, Dec 19 2012

Extensions

More terms from R. J. Mathar, Sep 27 2009