A347502 Number of dominating sets in the n-cycle complement graph.

0, -1, -1, 1, 9, 21, 51, 113, 239, 493, 1003, 2025, 4071, 8165, 16355, 32737, 65503, 131037, 262107, 524249, 1048535, 2097109, 4194259, 8388561, 16777167, 33554381, 67108811, 134217673, 268435399, 536870853, 1073741763, 2147483585, 4294967231, 8589934525

Offset: 0

Author

Eric W. Weisstein, Sep 04 2021

Keywords

• sign
• easy

Comments

Sequence extended to a(0) using the generating function.

Links

• Eric Weisstein's World of Mathematics, Cycle Complement Graph
• Eric Weisstein's World of Mathematics, Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A070313.

Formula

a(n) = A070313(n) = 2^n-2*n-1 for n != 4.

G.f.: x^3*(-1 - 5*x + 10*x^2 - 10*x^3 + 4*x^4)/((-1 + x)^2*(-1 + 2*x)).

E.g.f.: exp(2*x) + x^4/12 - exp(x)*(1 + 2*x). - Stefano Spezia, Sep 04 2021