OFFSET
1,2
COMMENTS
Main diagonal of the square array given in A132439.
a(n) is the number of Wythoff's Nim games starting with two equal piles of n stones. - Martin J. Erickson (erickson(AT)truman.edu), Dec 05 2008
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..300
M. Erickson, S. Fernando, K. Tran, Enumerating Rook and Queen Paths , Bulletin of the Institute for Combinatorics and Its Applications, Volume 60 (2010), 37-48.
FORMULA
G.f.: (x*(x-1)/(3*x-2))*(1 + (1-x)/sqrt(1 - 12*x + 16*x^2)). a(n) is asymptotic to (5^(3/4)*(sqrt(5)-2)/16)*(6+2*sqrt(5))^n/sqrt(Pi*n).
a(1)=1; a(2)=3; a(3)=22; a(4)=188; a(n) = ((29*n-47)*a(n-1) + (-95*n + 238)*a(n-2) + (116*n - 418)*a(n-3) + (-48*n + 240)*a(n-4))/(2*n-2), n >= 5. - Martin J. Erickson (erickson(AT)truman.edu), Nov 20 2007
EXAMPLE
a(2) = 3 since the paths from (1,1) to (2,2) are
(1,1)->(2,1)->(2,2),
(1,1)->(1,2)->(2,2),
(1,1)->(2,2).
MATHEMATICA
Rest[CoefficientList[Series[(x (x-1)/(3x-2))(1+(1-x)/Sqrt[1-12x+16x^2]), {x, 0, 20}], x]] (* Harvey P. Dale, Feb 09 2015 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Martin J. Erickson (erickson(AT)truman.edu), Nov 14 2007, Jan 28 2009
STATUS
approved