A177485 - OEIS

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A177485

G.f.: (1+x+x^3+x^5)/( (1-x^2+x^3)*(1-x-x^3) ).

1, 2, 3, 5, 7, 11, 15, 23, 32, 49, 69, 105, 149, 225, 321, 482, 691, 1033, 1487, 2215, 3199, 4751, 6880, 10193, 14793, 21873, 31801, 46945, 68353, 100770, 146899, 216333, 315671, 464467, 678287, 997287, 1457344, 2141473, 3131021, 4598617, 6726509, 9875521

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

This counts independent sets in certain graphs.

LINKS

Table of n, a(n) for n=0..41.

S. Kitaev and A. Burstein, Counting independent sets on path-schemes Journal of Integer Sequences 9, no. 2 (2006), Article 06.2.2

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,1).

EXAMPLE

For n=4, a(4)=7 because the graph is a cycle, and the independent sets are the empty set, {1}, {2}, {3}, {4}, {1,3} and {2,4}.

MATHEMATICA

CoefficientList[Series[(1+x+x^3+x^5)/( (1-x^2+x^3)*(1-x-x^3) ), {x, 0, 40}], x] (* Vaclav Kotesovec, Aug 25 2014 *)

LinearRecurrence[{1, 1, -1, 1, -1, 1}, {1, 2, 3, 5, 7, 11}, 50] (* Harvey P. Dale, Sep 22 2024 *)

PROG

(PARI) Vec((1+x+x^3+x^5)/((1-x^2+x^3)*(1-x-x^3)) + O(x^50)) \\ Michel Marcus, May 24 2015

CROSSREFS

Sequence in context: A052955 A326466 A326591 * A218023 A165801 A239054

Adjacent sequences: A177482 A177483 A177484 * A177486 A177487 A177488

KEYWORD

nonn,changed

AUTHOR

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

EXTENSIONS

Edited by N. J. A. Sloane, May 18 2010

More terms from Vaclav Kotesovec, Aug 25 2014

STATUS

approved