OFFSET
3,1
COMMENTS
A connected dominating set in the crown graph requires a minimum two vertices on each side of the graph which cannot be two pairs of opposing vertices. - Andrew Howroyd, Jun 03 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 3..200
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Crown Graph
Index entries for linear recurrences with constant coefficients, signature (11,-47,101,-116,68,-16).
FORMULA
a(n) = (2^n-n-1)^2 - n*(n-1)/2. - Andrew Howroyd, Jun 03 2017
From Colin Barker, Jun 03 2017: (Start)
G.f.: x^3*(13 - 28*x + 12*x^2) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)).
a(n) = 11*a(n-1) - 47*a(n-2) + 101*a(n-3) - 116*a(n-4) + 68*a(n-5) - 16*a(n-6) for n>8.
(End)
PROG
(PARI) Vec(x^3*(13 - 28*x + 12*x^2) / ((1 - x)^3*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Jun 03 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Eric W. Weisstein, May 25 2017
EXTENSIONS
Term a(13) and beyond from Andrew Howroyd, Jun 03 2017
STATUS
approved