A287497 - OEIS

%I #19 Feb 16 2025 08:33:46

%S 1,9,22,53,166,432,1212,3341,9175,25364,69829,192560,530830,1463170,

%T 4033687,11119101,30651528,84495213,232922084,642082488,1769987094,

%U 4879211973,13450215173,37077354584,102208799091,281752521488,776689338352,2141050324382

%N Number of maximal matchings in the n-web graph.

%C Extended to a(1)-a(2) using the formula.

%H Vincenzo Librandi, <a href="/A287497/b287497.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,3,-2,0,1).

%F a(n) = a(n-1)+4*a(n-2)+3*a(n-3)-2*a(n-4)+a(n-6).

%F G.f.: (x*(-1-8*x-9*x^2+8*x^3-6*x^5))/(-1+x+4*x^2+3*x^3-2*x^4+x^6).

%t LinearRecurrence[{1, 4, 3, -2, 0, 1}, {1, 9, 22, 53, 166, 432}, 20]

%t Rest @ CoefficientList[Series[(x (-1 - 8 x - 9 x^2 + 8 x^3 - 6 x^5))/(-1 + x + 4 x^2 + 3 x^3 - 2 x^4 + x^6), {x, 0, 20}], x]

%t Table[RootSum[-1 + 2 #^2 - 3 #^3 - 4 #^4 - #^5 + #^6 &, #^n &], {n, 20}]

%t RootSum[-1 + 2 #^2 - 3 #^3 - 4 #^4 - #^5 + #^6 &, #^Range[20] &] (* _Eric W. Weisstein_, Dec 30 2017 *)

%o (Magma) I:=[1,9,22,53,166,432]; [n le 6 select I[n] else Self(n-1)+4*Self(n-2)+3*Self(n-3)-2*Self(n-4)+Self(n-6): n in [1..30]]; // _Vincenzo Librandi_, Sep 03 2017

%K nonn

%O 1,2

%A _Eric W. Weisstein_, May 25 2017