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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also the 2nd row in the 2-shuffle Phi_2(W(sqrt(2)) of the Fraenkel-Kimberling publication. [R. J. Mathar, Aug 17 2009]. First differences of A056236. - Jeremy Gardiner, Aug 11 2013 LINKS Harry J. Smith, Table of n, a(n) for n=1,...,200 Tomislav Doslic, I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea 11 (2016) 255-276. International Mathematical Olympiad, 1979 Problem 6 A. S. Fraenkel, C. Kimberling, Generalized Wythoff arrays, shuffles and interspersions, Discr. Math. 126 (1-3) (1994) 137-149. [From R. J. Mathar, Aug 17 2009] Index entries for linear recurrences with constant coefficients, signature (4, -2). FORMULA G.f.: 2*x^2/(1-4*x+2*x^2). a(n) = (2 + sqrt(2))^(n-1)/sqrt(2) - (2-sqrt(2))^(n-1)/sqrt(2). a(n) = 4*a(n-1)-2*a(n-2). a(n) = 2*A007070(n-2) G.f.: G(0)/(2*x) - 1/x, where G(k)= 1 + 1/( 1 - 4*x^2/(4*x^2 + 2*(1-2*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(n-1, 4, 2)) for n in range(0, 24)] # Zerinvary Lajos, Nov 10 2009 CROSSREFS Sequence in context: A090426 A279193 A280279 * A106731 A318010 A291383 Adjacent sequences: A060992 A060993 A060994 * A060996 A060997 A060998 KEYWORD nonn AUTHOR Henry Bottomley, May 13 2001 STATUS approved

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Last modified December 6 08:34 EST 2023. Contains 367600 sequences. (Running on oeis4.)