A287471 Number of connected dominating sets in the n-crown graph.

13, 115, 666, 3234, 14379, 60981, 251968, 1026124, 4145241, 16670823, 66879606, 267944070, 1072693399, 4292739241, 17175150780, 68709515472, 274856935653, 1099467587835, 4397954236690, 17591993106730, 70368341524803, 281474137850205, 1125898162012536

Offset: 3

Author

Eric W. Weisstein, May 25 2017

Keywords

• nonn
• easy

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).

Programs

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

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)

Extensions

Term a(13) and beyond from Andrew Howroyd, Jun 03 2017