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A288038 Number of independent vertex sets in the n-Andrasfai graph. 1
3, 11, 33, 89, 225, 545, 1281, 2945, 6657, 14849, 32769, 71681, 155649, 335873, 720897, 1540097, 3276801, 6946817, 14680065, 30932993, 65011713, 136314881, 285212673, 595591169, 1241513985, 2583691265, 5368709121, 11140071425, 23085449217, 47781511169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The independence polynomial is given by I(n,x) = 1+(3*n-1)*x*(x+1)^(n-1).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Andrasfai Graph

Eric Weisstein's World of Mathematics, Independent Vertex Set

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

FORMULA

a(n) = 1 + (3*n-1)*2^(n-1).

From Colin Barker, Jun 05 2017: (Start)

G.f.: x*(3 - 4*x + 2*x^2) / ((1 - x)*(1 - 2*x)^2).

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n>3.

(End)

MATHEMATICA

Table[(3 n - 1) 2^(n - 1) + 1, {n, 20}]

LinearRecurrence[{5, -8, 4}, {3, 11, 33}, 20]

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

PROG

(PARI) Vec(x*(3 - 4*x + 2*x^2) / ((1 - x)*(1 - 2*x)^2) + O(x^30)) \\ Colin Barker, Jun 05 2017

(PARI) a(n) = 1 + (3*n-1)*2^(n-1); \\ Michel Marcus, Jun 05 2017

CROSSREFS

Sequence in context: A131747 A295626 A079996 * A186308 A352102 A171270

Adjacent sequences:  A288035 A288036 A288037 * A288039 A288040 A288041

KEYWORD

nonn,easy

AUTHOR

Andrew Howroyd, Jun 04 2017

STATUS

approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)