A386535 - OEIS

%I #42 Feb 03 2026 00:05:08

%S 7,76,997,13965,202828,2998629,44706045,669118516,10032719429,

%T 150553555885,2260093746588,33934103677157,509542394266397,

%U 7651380349411204,114896380194863173,1725345743467592269,25908806271341401836,389062474394973311845,5842404108398945690685

%N Number of independent vertex sets in the n-Lindgren-Sousselier graph.

%C Sequence extended to a(0) by the formula/recurrence.

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

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (21,-84,-87,-13,4).

%F a(n) = 21*a(n-1)-84*a(n-2)-87*a(n-3)-13*a(n-4)+4*a(n-5).

%F G.f.: -(7-71*x-11*x^2+21*x^3+14*x^4)/((1-7*x+x^2)*(-1+14*x+15*x^2+4*x^3)).

%t Table[2 ChebyshevT[2 n + 1, 3/2] - RootSum[-4 - 15 # - 14 #^2 + #^3 &, -8 #1^n - 15 #^(n + 1) + #^(n + 2) &]/2, {n, 0, 20}]

%t LinearRecurrence[{21, -84, -87, -13, 4}, {76, 997, 13965, 202828, 2998629}, {0, 20}]

%t CoefficientList[Series[-(7 - 71 x - 11 x^2 + 21 x^3 + 14 x^4)/((1 - 7 x + x^2) (-1 + 14 x + 15 x^2 + 4 x^3)), {x, 0, 20}], x]

%K nonn,easy

%O 0,1

%A _Eric W. Weisstein_, Sep 03 2025