A387596 - OEIS

%I #8 Sep 03 2025 01:37:26

%S 7,20,53,147,401,1105,3034,8349,22957,63155,173711,477852,1314449,

%T 3615799,9946297,27360297,75262642,207032537,569505065,1566594819,

%U 4309389479,11854270468,32608731853,89700113451,246747109345,678752052689,1867111432010,5136050915445

%N Number of maximum matchings in the n-Cameron graph.

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

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

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-5,1).

%F a(n) = 3*a(n-1)+a(n-2)-5*a(n-3)+a(n-4).

%F G.f.: (x*(-7+x+14*x^2-3*x^3))/(-1+3*x+x^2-5*x^3+x^4).

%t Table[RootSum[-1 + 5 # - #^2 - 3 #^3 + #^4 &, 74 #^n - 262 #^(n + 1) + 122 #^(n + 2) + 149 #^(n + 3) &]/1327, {n, 20}]

%t LinearRecurrence[{3, 1, -5, 1}, {7, 20, 53, 147}, 20]

%t CoefficientList[Series[(-7 + x + 14 x^2 - 3 x^3)/(-1 + 3 x + x^2 - 5 x^3 + x^4), {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Sep 02 2025