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A025178
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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(n), |s(1)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2. Also a(n) = T(n,n), where T is the array defined in A025177.
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1
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2, 4, 12, 32, 90, 252, 714, 2032, 5814, 16700, 48136, 139152, 403286, 1171380, 3409020, 9938304, 29017878, 84844044, 248382516, 727971360, 2135784798, 6272092596, 18435108258, 54228499920, 159636389850, 470256930052, 1386170197704
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OFFSET
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2,1
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COMMENTS
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First differences of the central trinomial coefficients A002426. Note that n-1 divides a(n). - T. D. Noe, Mar 16 2005
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LINKS
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Table of n, a(n) for n=2..28.
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FORMULA
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a(n) = A002426(n+1)-A002426(n); a(n) is asymptotic to c*3^n/sqrt(n) with c around 1.02... - Benoit Cloitre, Nov 02, 2002
a(n) = 2*(n-1)*A001006(n-2). - M. F. Hasler, Oct 24 2011
a(n) = 2*A005717(n-1). - R. J. Mathar, Jul 09 2012
E.g.f. 2*exp(x)*((1-1/x)*BesselI(1,2*x) + 2*BesselI(0,2*x)). - Sergei N. Gladkovskii, Aug 16 2012
G.f.: -1/x^2 + (1/x^2 - 1/x)/sqrt(1-2*x-3*x^2). - Sergei N. Gladkovskii, Aug 16 2012
a(n) = (2*n+3)/(n+2)*a(n-1) + (3*n^3+3*n^2-n-4)/((n-1)*(n+1)*(n+2))*a(n-2) + 3/((n+1)*(n+2))*a(n-3), a(0)=2, a(1)=4, a(2)=12. - Sergei N. Gladkovskii, Aug 16 2012
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MATHEMATICA
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Rest[Differences[CoefficientList[Series[ 1/Sqrt[1-2x-3x^2], {x, 0, 30}], x]]] (* From Harvey P. Dale, Aug 22 2011 *)
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CROSSREFS
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Sequence in context: A028860 A152035 A026151 * A087211 A161177 A039721
Adjacent sequences: A025175 A025176 A025177 * A025179 A025180 A025181
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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