This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A235115 Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the star graph S_n (having n vertices; see A235114). 2
 5, 24, 116, 564, 2756, 13524, 66596, 328884, 1628036, 8074644, 40111076, 199506804, 993339716, 4949921364, 24682497956, 123144054324, 614646529796, 3068937681684, 15327508539236, 76568823219444, 382569238190276, 1911746679323604, 9554335350106916, 47754084564490164, 238700054078273156 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the sum of the entries of row n of the triangle A235114. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 E. Mandrescu, Unimodality of some independence polynomials via their palindromicity, Australasian J. of Combinatorics, 53, 2012, 77-82. D. Stevanovic, Graphs with palindromic independence polynomial, Graph Theory Notes of New  York, 34, 1998, 31-36. Index entries for linear recurrences with constant coefficients, signature (9,-20). FORMULA a(n) = 4*5^(n-1) + 2^(2*n-2) for n>=1. G.f.: x*(5 - 21*x)/((1 - 4*x)*(1 - 5*x)). a(n) = 9*a(n-1) - 20*a(n-2) for n>1. - Colin Barker, Jul 31 2017 EXAMPLE a(1)=5; indeed, S_1 is the one-vertex graph and after attaching two pendant vertices we obtain the path graph ABC; the independent vertex subsets are: empty, {A}, {B}, {C}, and {A,C}. MAPLE seq(4*5^(n-1)+2^(2*n-2), n = 1 .. 27); MATHEMATICA Rest@ CoefficientList[Series[x (5 - 21 x)/((1 - 4 x) (1 - 5 x)), {x, 0, 25}], x] (* or *) LinearRecurrence[{9, -20}, {5, 24}, 25] (* Michael De Vlieger, Jul 31 2017 *) PROG (PARI) Vec(x*(5 - 21*x) / ((1 - 4*x)*(1 - 5*x)) + O(x^30)) \\ Colin Barker, Jul 31 2017 (MAGMA) [4*5^(n-1)+2^(2*n-2): n in [1..25]]; // Vincenzo Librandi, Aug 01 2017 CROSSREFS Cf. A235118. Sequence in context: A086347 A200739 A026707 * A110190 A026784 A017977 Adjacent sequences:  A235112 A235113 A235114 * A235116 A235117 A235118 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jan 13 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 18 14:59 EST 2019. Contains 329262 sequences. (Running on oeis4.)