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 A152132 Maximal length of rook tour on an n X n+1 board. 9
 2, 8, 24, 54, 104, 174, 270, 396, 558, 756, 996, 1282, 1620, 2010, 2458, 2968, 3546, 4192, 4912, 5710, 6592, 7558, 8614, 9764, 11014, 12364, 13820, 15386, 17068, 18866, 20786, 22832, 25010, 27320, 29768, 32358, 35096, 37982, 41022, 44220, 47582 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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). FORMULA G.f.: -2*x*(-1-x-2*x^3-2*x^4-3*x^2+x^5)/(1+x)/(x^2+1)/(x-1)^4. 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). a(n) = 2*n^3/3+n^2-7*n/6+3/4-(-1)^n/4-A087960(n)/2. MAPLE # Figure 43 of the Gardner book: C := proc(n, m) if type(m, even) and type(n, even) then 2 ; elif type(m, odd) and type(n, odd) then 1 ; elif type(m, even) and type(n, odd) and type(floor(n/2), even) then 3/2 ; elif type(m, even) and type(n, odd) and type(floor(n/2), odd) then 1/2 ; elif type(m, odd) and type(n, even) and type(floor(n/2), even) then 0 ; elif type(m, odd) and type(n, even) and type(floor(n/2), odd) then 1 ; fi; end: # formula for n X m boards, from the Gardner book: T := proc(n, m) n*(3*m^2+n^2-10)/6+C(n, m) ; end: for n from 1 to 24 do m := n+3 ; # third diagonal here, for example printf("%d, ", T(n, m)) ; od: MATHEMATICA CoefficientList[Series[-2 * (-1 - x - 2*x^3 - 2*x^4 - 3*x^2 + x^5)/(1 + x)/(x^2 + 1)/(x - 1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 14 2012 *) PROG (MAGMA) I:=[2, 8, 24, 54, 104, 174, 270]; [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..50]]; // Vincenzo Librandi, Dec 14 2012 CROSSREFS Cf. A006071, A152133-A152135. Sequence in context: A171261 A084744 A122547 * A330520 A009059 A009297 Adjacent sequences:  A152129 A152130 A152131 * A152133 A152134 A152135 KEYWORD nonn,easy AUTHOR R. J. Mathar, Mar 22 2009 EXTENSIONS More terms from R. J. Mathar, Sep 22 2009 STATUS approved

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Last modified April 17 23:03 EDT 2021. Contains 343071 sequences. (Running on oeis4.)