A036757 - OEIS

%I #22 Jan 30 2020 21:29:14

%S 1,1,2,7,26,126,640,3559,20366,120535,727292,4468614,27842644,

%T 175644673,1119847820,7207062667,46769169830,305762838483,

%U 2012363156332,13324398048658,88709165046956,593555082569368,3989727169508528

%N Number of tree-like heptagonal systems.

%D S. J. Cyvin, B. N. Cyvin, and J. Brunvoll. Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), 55-70.

%H Vincenzo Librandi, <a href="/A036757/b036757.txt">Table of n, a(n) for n = 1..500</a>

%H J. Brunvoll et al., <a href="http://dx.doi.org/10.1023/A:1019122419384">Enumeration of tree-like octagonal systems</a>, J. Math. Chem., 21 (1997), 193-196.

%F G.f.: (1/x^4)*((x^2/54)*(5+12*x-27*x^2+16*x^3+3*x^4+(1/4)*(1-8*x+4*x^2)^(3/2)-(3/4)*(7+12*x+2*x^2)*(1-8*x^2+4*x^4)^(1/2))). - Adjusted for shift by _Enxhell Luzhnica_, Jan 20 2017

%F D-finite with recurrence: -2*(37333940645327033*n -118246388381321724)*(n+2)*(n+1)*a(n) +(n+1)*(713264163292482871*n^2 -2924046469427413489*n +1162756152416330286)*a(n-1) +4*(-152996351532211558*n^3 +1720662676274714640*n^2 -2533776489355639049*n -59123194190660862)*a(n-2) +4*(-1342943576342180377*n^3 +7608046315696084062*n^2 -13914387232583975999*n +9124977747699642762)*a(n-3) +8*(1176000173357559779*n^3 -12080777098370225883*n^2 +41059366674368812519*n -46837520282616567774)*a(n-4) +4*(48936490024662023*n^3 +4102665980343195888*n^2 -45578929167175613951*n +116638160879966581764)*a(n-5) +32*(-159177372154375949*n^3 +1844748442783980714*n^2 -4261065176440884304*n -6098129046823314687)*a(n-6) +16*(74884092893861221*n^3 -1252855905292173702*n^2 +6404002902490756322*n -8555019969894216645)*a(n-7) +64*(n-10)*(2002828774404026*n^2 +53787805034972963*n -566190782987287023)*a(n-8) +192*(n-10)*(n-11)*(362527389538506*n -7714335008857429)*a(n-9)=0. - _R. J. Mathar_, Jan 28 2020

%p (5+12*x-27*x^2+16*x^3+3*x^4+(1/4)*(1-8*x+4*x^2)^(3/2)-(3/4)*(7+12*x+2*x^2)*(1-8*x^2+4*x^4)^(1/2))/(54*x^2);

%p taylor(%,x=0,30) ;

%p gfun[seriestolist](%) ; # _R. J. Mathar_, Jul 28 2019

%t Rest[CoefficientList[Series[(1/x^4) ((x^2/54) (5 + 12 x - 27 x^2 + 16 x^3 + 3 x^4 + (1/4) (1 - 8 x + 4 x^2)^(3/2) - (3/4) (7 + 12 x + 2 x^2) (1 - 8 x^2 + 4 x^4)^(1/2))), {x, 0, 30}], x]]; (* _Vincenzo Librandi_, Jan 21 2017 *)

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_.

%E More terms from _Emeric Deutsch_, Feb 28 2004