A036757 Number of tree-like heptagonal systems.

1, 1, 2, 7, 26, 126, 640, 3559, 20366, 120535, 727292, 4468614, 27842644, 175644673, 1119847820, 7207062667, 46769169830, 305762838483, 2012363156332, 13324398048658, 88709165046956, 593555082569368, 3989727169508528

Offset

1,3

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..500

J. Brunvoll et al., Enumeration of tree-like octagonal systems, J. Math. Chem., 21 (1997), 193-196.

Formula

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

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

Maple

(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);
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ; # R. J. Mathar, Jul 28 2019

Mathematica

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 *)

Crossrefs

Sequence in context: A141203 A346749 A096803 * A358493 A341900 A300049

Adjacent sequences: A036754 A036755 A036756 * A036758 A036759 A036760

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Emeric Deutsch, Feb 28 2004

Status

approved