OFFSET
1,3
COMMENTS
In a total dominating set each side of the crown graph requires any two vertices on the other side to dominate it. - Andrew Howroyd, Apr 16 2018
LINKS
Eric Weisstein's World of Mathematics, Crown Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
Index entries for linear recurrences with constant coefficients, signature (11,-47,101,-116,68,-16).
FORMULA
a(n) = (2^n - 1 - n)^2. - Andrew Howroyd, Apr 16 2018
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).
G.f.: x^2*(1 + 5*x - 8*x^2 - 4*x^3)/((-1 + x)^3*(-1 + 2*x)^2*(-1 + 4*x)).
MATHEMATICA
Table[(1 - 2^n + n)^2, {n, 20}]
LinearRecurrence[{11, -47, 101, -116, 68, -16}, {0, 1, 16, 121, 676, 3249}, 20]
CoefficientList[Series[x (1 + 5 x - 8 x^2 - 4 x^3)/((-1 + x)^3 (-1 + 2 x)^2 (-1 + 4 x)), {x, 0, 20}], x]
PROG
(PARI) a(n)=(2^n-1-n)^2; \\ Andrew Howroyd, Apr 16 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 16 2018
EXTENSIONS
a(1)-a(2) and a(11)-a(25) from Andrew Howroyd, Apr 16 2018
STATUS
approved