OFFSET
1,1
COMMENTS
Recurrence used to extrapolate sequence to a(1) and a(2).
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Dominating Set
Index entries for linear recurrences with constant coefficients, signature (3,3,1,1,1).
FORMULA
From Colin Barker, Apr 01 2017: (Start)
G.f.: x*(3 + 6*x + 3*x^2 + 4*x^3 + 5*x^4) / (1 - 3*x - 3*x^2 - x^3 - x^4 - x^5).
a(n) = 3*a(n-1) + 3*a(n-2) + a(n-3) + a(n-4) + a(n-5) for n>5.
(End)
MATHEMATICA
LinearRecurrence[{3, 3, 1, 1, 1}, {3, 15, 57, 223, 863, 3333, 12883}, 20]
Table[RootSum[-1 - # - #^2 - 3 #^3 - 3 #^4 + #^5 &, #^n &], {n, 20}]
PROG
(PARI) Vec(x*(3 + 6*x + 3*x^2 + 4*x^3 + 5*x^4) / (1 - 3*x - 3*x^2 - x^3 - x^4 - x^5) + O(x^30)) \\ Colin Barker, Apr 01 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 01 2017
STATUS
approved