A386535 Number of independent vertex sets in the n-Lindgren-Sousselier graph.

7, 76, 997, 13965, 202828, 2998629, 44706045, 669118516, 10032719429, 150553555885, 2260093746588, 33934103677157, 509542394266397, 7651380349411204, 114896380194863173, 1725345743467592269, 25908806271341401836, 389062474394973311845, 5842404108398945690685

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Independent Vertex Set.

Eric Weisstein's World of Mathematics, Lindgren-Sousselier Graphs.

Index entries for linear recurrences with constant coefficients, signature (21,-84,-87,-13,4).

Formula

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

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)).

Mathematica

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

Crossrefs

Sequence in context: A098497 A385474 A366015 * A380972 A384983 A337595

Adjacent sequences: A386532 A386533 A386534 * A386536 A386537 A386538

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 03 2025

Status

approved