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Search: id:A060899
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| A060899 |
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Number of walks of length n on square lattice, starting at origin, staying on points with x+y >= 0. |
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2
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| 1, 2, 8, 24, 96, 320, 1280, 4480, 17920, 64512, 258048, 946176, 3784704, 14057472, 56229888, 210862080, 843448320, 3186360320, 12745441280, 48432676864, 193730707456, 739699064832, 2958796259328, 11342052327424
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,200
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FORMULA
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a(n) = 2^n*binomial(n, [n/2]);
G.f.: (sqrt((1+4*x)/(1-4*x))-1)/4/x. - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2003
E.g.f.: BesselI(0, 4*x)+BesselI(1, 4*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 28 2003
a(n)=4^n*sum{k=0..n, C(n,k)C(k)/(-2)^k}, with C(n)=A00108(n). - Paul Barry (pbarry(AT)wit.ie), Dec 28 2006
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PROGRAM
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(PARI) { for (n=0, 200, write("b060899.txt", n, " ", 2^n*binomial(n, n\2)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 14 2009]
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CROSSREFS
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Cf. A005566, A001700, A060897-A060900.
Cf. A001405.
Sequence in context: A007223 A106189 A106183 this_sequence A150665 A150666 A150667
Adjacent sequences: A060896 A060897 A060898 this_sequence A060900 A060901 A060902
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net), May 05 2001
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