A347512 Number of minimal dominating sets in the n-book graph.

6, 7, 11, 19, 35, 67, 131, 259, 515, 1027, 2051, 4099, 8195, 16387, 32771, 65539, 131075, 262147, 524291, 1048579, 2097155, 4194307, 8388611, 16777219, 33554435, 67108867, 134217731, 268435459, 536870915, 1073741827, 2147483651, 4294967299, 8589934595

Offset: 1

Author

Eric W. Weisstein, Sep 04 2021

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Book Graph
• Eric Weisstein's World of Mathematics, Minimal Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A062709 (essentially the same).

Programs

Mathematica

Join[{6}, 2^Range[2, 20] + 3]
CoefficientList[Series[(6 - 11 x + 2 x^2)/((-1 + x) (-1 + 2 x)), {x, 0, 20}], x]

Formula

a(n) = A062709(n) = 2^n + 3 for n > 1.

G.f.: x*(6 - 11*x + 2*x^2)/((-1 + x)*(-1 + 2*x)).

E.g.f.: exp(x)*(3 + exp(x)) - 4 + x. - Stefano Spezia, Sep 04 2021