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A005775
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Number of compact-rooted directed animals of size n having 3 source points.
(Formerly M3481)
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1
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1, 4, 14, 45, 140, 427, 1288, 3858, 11505, 34210, 101530, 300950, 891345, 2638650, 7809000, 23107488, 68375547, 202336092, 598817490, 1772479905, 5247421410, 15538054455, 46019183840, 136325212750, 403933918375, 1197131976846
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| Binomial transform of A037955. - Paul Barry (pbarry(AT)wit.ie), Dec 28 2006
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REFERENCES
| D. Gouyou-Beauchamps; G. Viennot, Equivalence of the two-dimensional directed animal problem to a one-dimensional path problem, Adv. in Appl. Math. 9 (1988), no. 3, 334-357.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| (n+2)(n-3)a(n) = 2n(n-1)a(n-1)+3(n-1)(n-2)a(n-2), a(2)=0, a(3)=1. - Michael Somos, Feb 02, 2002
G.f.: (x^2+x-1 +(x^2-3*x+1)*sqrt((1+x)/(1-3*x)))/(2*x^2).
E.g.f.: exp(x)(Bessel_I(2,2x)+Bessel_I(3,2x)); a(n)=sum{k=0..n, C(n,k)C(n,floor(n/2)-1)}; - Paul Barry (pbarry(AT)wit.ie), Dec 28 2006
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PROG
| (PARI) a(n)=polcoeff((x^2+x-1 +(x^2-3*x+1)*sqrt((1+x)/(1-3*x)+x^3*O(x^n)))/(2*x^2), n)
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CROSSREFS
| Cf. A005773.
k=2 column of array in A038622.
Sequence in context: A184138 A182902 A108765 * A094688 A068092 A153480
Adjacent sequences: A005772 A005773 A005774 * A005776 A005777 A005778
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KEYWORD
| nonn,easy
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AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Randall L. Rathbun, Jan 19 2002
Edited by Michael Somos, Feb 02, 2002
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