A045635 - OEIS

%I #22 Oct 23 2022 16:34:52

%S 0,0,1,9,57,315,1629,8127,39718,191754,919035,4385799,20879100,

%T 99276840,471848195,2242864575,10665998760,50757180840,241743946635,

%U 1152434818755,5499250360025,26268118117731,125602004765391

%N Catafusenes (see references for precise definition).

%C The sequence without the initial 0's is the 3-fold convolution of A002212(n), (n=1,2,...). - _Emeric Deutsch_, Mar 13 2004

%H B. N. Cyvin et al., <a href="https://dx.doi.org/10.1007/BF00811082">A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes</a>, Monat. f. Chemie, 125 (1994), 1327-1337.

%H S. J. Cyvin et al., <a href="https://dx.doi.org/10.1021/ci00021a026">Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes</a>, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.

%F G.f.: (zM)^3, where M = (1 - 3*z - sqrt(1 - 6*z + 5*z^2))/(2*z^2). - _Emeric Deutsch_, Mar 13 2004

%F 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

%F a(n) = A003517(n) * hypergeom([-n - 4, 2 - n], [-n - 1/2], -1/4). - _Peter Luschny_, Oct 23 2022

%p 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

%p a := n -> A003517(n) * hypergeom([-n - 4, 2 - n], [-n - 1/2], -1/4):

%p seq(simplify(a(n)), n = 0..22); # _Peter Luschny_, Oct 23 2022

%Y Cf. A002212, A003517.

%K nonn

%O 1,4

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Mar 13 2004