

A060995


Number of routes of length 2n on the sides of an octagon from a point to opposite point.


5



0, 2, 8, 28, 96, 328, 1120, 3824, 13056, 44576, 152192, 519616, 1774080, 6057088, 20680192, 70606592, 241065984, 823050752, 2810071040, 9594182656, 32756588544, 111837988864, 381838778368, 1303679135744
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OFFSET

1,2


COMMENTS

Also the 2nd row in the 2shuffle Phi_2(W(sqrt(2)) of the FraenkelKimberling publication. [R. J. Mathar, Aug 17 2009].


LINKS



FORMULA

G.f.: 2*x^2/(14*x+2*x^2).
a(n) = (2 + sqrt(2))^(n1)/sqrt(2)  (2sqrt(2))^(n1)/sqrt(2).
a(n) = 4*a(n1)2*a(n2).
G.f.: G(0)/(2*x)  1/x, where G(k)= 1 + 1/( 1  4*x^2/(4*x^2 + 2*(12*x)^2/G(k+1) )); (continued fraction).  Sergei N. Gladkovskii, Jul 16 2013


MATHEMATICA

LinearRecurrence[{4, 2}, {0, 2}, 40] (* Harvey P. Dale, Mar 03 2012 *)


PROG

(PARI) { for (n=1, 200, if (n>2, a=4*a1  2*a2; a2=a1; a1=a, if (n==1, a=a2=0, a=a1=2)); write("b060995.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 16 2009
(Sage) [(lucas_number2(n, 4, 2)lucas_number2(n1, 4, 2)) for n in range(0, 24)] # Zerinvary Lajos, Nov 10 2009


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



