OFFSET
1,1
COMMENTS
Sequence extrapolated to a(1) and a(2) using recurrence. - Andrew Howroyd, Sep 04 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (6, -11, 4, 5, -2, -1).
FORMULA
From Andrew Howroyd, Sep 04 2017: (Start)
a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6) for n > 6.
G.f.: x*(7 - 35*x + 74*x^2 - 70*x^3 + 19*x^4 - 3*x^5)/((1 - x)^2*(1 - 2*x - x^2)^2).
(End)
MATHEMATICA
Rest @ CoefficientList[Series[x (7 - 35 x + 74 x^2 - 70 x^3 + 19 x^4 - 3 x^5)/((1 - x)^2*(1 - 2 x - x^2)^2), {x, 0, 28}], x] (* Michael De Vlieger, Sep 04 2017 *)
Table[LucasL[n, 2] + 2 n (3 Fibonacci[n - 2, 2] + Fibonacci[n - 1, 2] - 1) + 1, {n, 20}] (* Eric W. Weisstein, Sep 08 2017 *)
LinearRecurrence[{6, -11, 4, 5, -2, -1}, {7, 7, 39, 115, 343, 967}, 20] (* Eric W. Weisstein, Sep 08 2017 *)
PROG
(PARI) Vec((7 - 35*x + 74*x^2 - 70*x^3 + 19*x^4 - 3*x^5)/((1 - x)^2*(1 - 2*x - x^2)^2) + O(x^30))
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, May 17 2017
EXTENSIONS
a(1)-a(2) and terms a(14) and beyond from Andrew Howroyd, Sep 04 2017
STATUS
approved