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 A045635 Catafusenes (see references for precise definition). 0
 0, 0, 1, 9, 57, 315, 1629, 8127, 39718, 191754, 919035, 4385799, 20879100, 99276840, 471848195, 2242864575, 10665998760, 50757180840, 241743946635, 1152434818755, 5499250360025, 26268118117731, 125602004765391 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The sequence without the initial 0's is the 3-fold convolution of A002212(n), (n=1,2,...). - Emeric Deutsch, Mar 13 2004 LINKS Table of n, a(n) for n=1..23. B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes, Monat. f. Chemie, 125 (1994), 1327-1337. S. J. Cyvin et al., Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180. FORMULA G.f.: (zM)^3, where M = (1 - 3*z - sqrt(1 - 6*z + 5*z^2))/(2*z^2). - Emeric Deutsch, Mar 13 2004 a(n) = (3/(n+1))*Sum_{m=0..n-2} C(n+1,m)*C(2*n-2*m+2,n-m-2). - Vladimir Kruchinin Oct 18 2022 a(n) = A003517(n) * hypergeom([-n - 4, 2 - n], [-n - 1/2], -1/4). - Peter Luschny, Oct 23 2022 MAPLE Z:=(1-8*z+24*z^2-16*z^3-(1-6*z+8*z^2)*sqrt(1-6*z+5*z^2))/2: Zser:=series(Z, z=0, 32): seq(coeff(Zser, z, n), n=4..26); # Zerinvary Lajos, Jan 01 2007 a := n -> A003517(n) * hypergeom([-n - 4, 2 - n], [-n - 1/2], -1/4): seq(simplify(a(n)), n = 0..22); # Peter Luschny, Oct 23 2022 CROSSREFS Cf. A002212, A003517. Sequence in context: A192054 A045720 A014916 * A026896 A080961 A163919 Adjacent sequences: A045632 A045633 A045634 * A045636 A045637 A045638 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Emeric Deutsch, Mar 13 2004 STATUS approved

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Last modified March 1 15:29 EST 2024. Contains 370440 sequences. (Running on oeis4.)