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A303005
Number of dominating sets in the n-pan graph.
3
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
Eric Weisstein's World of Mathematics, Dominating Set
Eric Weisstein's World of Mathematics, Pan Graph
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 17 2018
STATUS
approved