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A296995 Number of edge covers in the n-dipyramidal graph. 3

%I #15 Jun 27 2018 08:44:08

%S 2,34,341,2902,23092,178393,1359598,10296846,77752133,586292914,

%T 4418053928,33282217873,250685741074,1888064403826,14219675836741,

%U 107091705316446,806526755213324,6074075885446057,45744715781412614,344509590254476102,2594546978760459973

%N Number of edge covers in the n-dipyramidal graph.

%C Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Jun 26 2018

%H Andrew Howroyd, <a href="/A296995/b296995.txt">Table of n, a(n) for n = 1..200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11, -24, -21, 33, 34, 8).

%F From _Andrew Howroyd_, Jun 26 2018: (Start)

%F a(n) = 11*a(n-1) - 24*a(n-2) - 21*a(n-3) + 33*a(n-4) + 34*a(n-5) + 8*a(n-6) for n > 6.

%F G.f.: x*(2 + 2*x + x^2)*(1 + 5*x + 2*x^2)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)). (End)

%t Table[LucasL[n] + 2^-n ((7 - Sqrt[65])^n + (7 + Sqrt[65])^n) - 2^(-n + 1) ((3 - Sqrt[17])^n + (3 + Sqrt[17])^n), {n, 20}] // Expand

%t LinearRecurrence[{11, -24, -21, 33, 34, 8}, {2, 34, 341, 2902, 23092, 178393}, 20]

%t CoefficientList[Series[(-2 - 12 x - 15 x^2 - 9 x^3 - 2 x^4)/(-1 + 11 x - 24 x^2 - 21 x^3 + 33 x^4 + 34 x^5 + 8 x^6), {x, 0, 20}], x]

%o (PARI) Vec((2 + 2*x + x^2)*(1 + 5*x + 2*x^2)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)) + O(x^30)) \\ _Andrew Howroyd_, Jun 26 2018

%Y Cf. A297713, A298822.

%K nonn

%O 1,1

%A _Eric W. Weisstein_, Jun 18 2018

%E a(1)-a(2) and terms a(11) and beyond from _Andrew Howroyd_, Jun 26 2018

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)