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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 xrange(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 March 22 01:06 EDT 2019. Contains 321406 sequences. (Running on oeis4.)