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

Author

N. J. A. Sloane, Aug 13 2006

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

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

Programs

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 *)

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

Extensions

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