A303005 Number of dominating sets in the n-pan graph.

3, 5, 11, 19, 35, 65, 119, 219, 403, 741, 1363, 2507, 4611, 8481, 15599, 28691, 52771, 97061, 178523, 328355, 603939, 1110817, 2043111, 3757867, 6911795, 12712773, 23382435, 43007003, 79102211, 145491649, 267600863, 492194723, 905287235, 1665082821, 3062564779, 5632934835

Offset

1,1

Comments

Extended to a(1)-a(2) using the formula/recurrence.

Links

Table of n, a(n) for n=1..36.

Eric Weisstein's World of Mathematics, Dominating Set

Eric Weisstein's World of Mathematics, Pan Graph

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

Formula

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

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

Maple

A303005 := proc(n)
    option remember;
    if n < 4 then
        op(n, [3, 5, 11]) ;
    else
        procname(n-1)+procname(n-2)+procname(n-3) ;
    end if;
end proc:
seq(A303005(n), n=1..30) ; # R. J. Mathar, Jan 11 2024

Mathematica

Table[RootSum[-1 - # - #^2 + #^3 &, #^n (7 - 3 # + 5 #^2) &]/11, {n, 20}]
LinearRecurrence[{1, 1, 1}, {3, 5, 11}, 20]
CoefficientList[Series[(-3 - 2 x - 3 x^2)/(-1 + x + x^2 + x^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A239519 A329178 A298348 * A320790 A175783 A078722

Adjacent sequences: A303002 A303003 A303004 * A303006 A303007 A303008

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 17 2018

Status

approved