A121134 - OEIS

%I #18 May 14 2024 03:34:46

%S 1,2,5,11,30,72,182,434,1048,2456,5752,13240,30336,68736,154912,

%T 346400,770688,1704576,3753344,8226176,17959936,39062528,84679168,

%U 182983168,394278912,847263744,1816164352,3883956224,8288010240,17649696768

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

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

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8,-16,44,-8,-48,32).

%F G.f.: x*(8*x^9+4*x^8-18*x^7-10*x^6+20*x^5+8*x^4-13*x^3-x^2+4*x-1) / ((2*x-1)^3*(2*x^2-1)^2). - _Colin Barker_, Nov 30 2012

%p 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: A121134 := proc(n) Ifunc(n,2,5) ; end: for n from 2 to 80 do printf("%d,",A121134(n)) ; od: # _R. J. Mathar_, Aug 07 2008

%K nonn,easy

%O 2,2

%A _N. J. A. Sloane_, Aug 13 2006

%E Extended beyond a(10) by _R. J. Mathar_, Aug 07 2008