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A036757
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Number of tree-like heptagonal systems.
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1
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1, 1, 2, 7, 26, 126, 640, 3559, 20366, 120535, 727292, 4468614, 27842644, 175644673, 1119847820, 7207062667, 46769169830, 305762838483, 2012363156332, 13324398048658, 88709165046956, 593555082569368, 3989727169508528
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OFFSET
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1,3
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REFERENCES
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S. J. Cyvin, B. N. Cyvin, and J. Brunvoll. Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), 55-70.
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LINKS
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FORMULA
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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
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MAPLE
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(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) ;
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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