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Search: id:A025179
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| A025179 |
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a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is an integer, s(0) = 0, |s(1)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2, s(n) = 1. Also a(n) = T(n,n-1), where T is the array defined in A025177. |
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5
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| 1, 4, 10, 29, 81, 231, 659, 1891, 5443, 15718, 45508, 132067, 384047, 1118820, 3264642, 9539787, 27913083, 81769236, 239794422, 703906719, 2068153899, 6081507831, 17896695831, 52703944965, 155310270101, 457956633826, 1351132539604
(list; graph; listen)
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OFFSET
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2,2
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FORMULA
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Sum_{k=0..floor(n/2)} binomial(n, 2*k)*binomial(2*k+1, k+1). E.g.f.: exp(x)*(BesselI(0, 2*x)+BesselI(2, 2*x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 01 2004
G.f.: ((1-x)^2-(1-x)sqrt(1-2x-3x^2))/(2x*sqrt(1-2x-3x^2)); a(n+1)=sum{k=0..n, C(n, k)C(k+1, k/2+1)(1+(-1)^k)/2}; - Paul Barry (pbarry(AT)wit.ie), Sep 17 2005
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CROSSREFS
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Equals (1/2) * A024997. Cf. A026135.
Sequence in context: A006907 A052946 A026152 this_sequence A116388 A152808 A151874
Adjacent sequences: A025176 A025177 A025178 this_sequence A025180 A025181 A025182
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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