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A060995
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Number of routes of length 2n on the sides of an octagon from a point to opposite point.
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4
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also the 2nd row in the 2-shuffle Phi_2(W(sqrt(2)) of the Fraenkel-Kimberling publication. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,200
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 (mathar(AT)strw.leidenuniv.nl), Aug 17 2009]
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FORMULA
| G.f.: 2x^2/(1-4x+2x^2).
a(n) = (2 + sqrt(2))^(n-1)/sqrt(2)-(2-sqrt(2))^(n-1)/sqrt(2) = 4a(n-1)-2a(n-2) = 2*A007070(n-2)
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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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 16 2009]
(Other) sage: [(lucas_number2(n, 4, 2)-lucas_number2(n-1, 4, 2)) for n in xrange(0, 24)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
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CROSSREFS
| Sequence in context: A176758 A178222 A090426 * A106731 A066796 A104934
Adjacent sequences: A060992 A060993 A060994 * A060996 A060997 A060998
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 13 2001
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