A121136 Numbers of isomers of unbranched a-4-catapolypentagons - see Brunvoll reference for precise definition.

1, 3, 13, 45, 164, 527, 1652, 4876, 14000, 38800, 105112, 278104, 722736, 1846320, 4650368, 11560320, 28413312, 69111168, 166551680, 397975680, 943672576, 2221821184, 5197313024, 12084884480, 27944656896, 64286203904, 147182565376

Offset

4,2

Links

Table of n, a(n) for n=4..30.

J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13.

Index entries for linear recurrences with constant coefficients, signature (10,-34,20,148,-328,8,688,-640,-256,640,-256).

Formula

G.f.: x^4 * (64*x^13 -32*x^12 -192*x^11 +128*x^10 +212*x^9 -172*x^8 -114*x^7 +110*x^6 +41*x^5 -52*x^4 -3*x^3 +17*x^2 -7*x+1) / ((2*x-1)^5 * (2*x^2-1)^3). - Colin Barker, Nov 30 2012

Maple

H := proc(r, alpha, q) local rhalf, alphahalf ; rhalf := floor(r/2) ; alphahalf := floor(alpha/2) ; (binomial(rhalf-1, alphahalf-1)*(q-3) +binomial(rhalf-1, alphahalf))*(q-3)^(rhalf-alphahalf-1) ; end: J := proc(r, alpha, q) (binomial(r-2, alpha-2)*(q-3)^2+2*binomial(r-2, alpha-1) *(q-3)+binomial(r-2, alpha))*(q-3)^(r-alpha-2) ; end: Ifunc := proc(r, alpha, q) J(r, alpha, q)/4+binomial(2, r-alpha)/4+ (1+(-1)^(r+alpha) +(1+(-1)^alpha)*(1-(-1)^r)/2)*H(r, alpha, q)/4 ; end: A121136 := proc(n) Ifunc(n, 4, 5) ; end: for n from 4 to 80 do printf("%d, ", A121136(n)) ; od: # R. J. Mathar, Aug 07 2008

Mathematica

Join[{1, 3, 13}, LinearRecurrence[{10, -34, 20, 148, -328, 8, 688, -640, -256, 640, -256}, {45, 164, 527, 1652, 4876, 14000, 38800, 105112, 278104, 722736, 1846320}, 24]] (* Jean-François Alcover, Mar 31 2020 *)

Crossrefs

Cf. A121133. - R. J. Mathar, Aug 07 2008

Sequence in context: A140420 A308087 A232231 * A350175 A239592 A017943

Adjacent sequences: A121133 A121134 A121135 * A121137 A121138 A121139

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 13 2006

Extensions

Extended beyond a(10) by R. J. Mathar, Aug 07 2008

Status

approved