A347501 Number of dominating sets in the n-alkane graph.

17, 81, 405, 2025, 10125, 50625, 253125, 1265625, 6328125, 31640625, 158203125, 791015625, 3955078125, 19775390625, 98876953125, 494384765625, 2471923828125, 12359619140625, 61798095703125, 308990478515625, 1544952392578125, 7724761962890625

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Alkane Graph

Eric Weisstein's World of Mathematics, Dominating Set

Index entries for linear recurrences with constant coefficients, signature (5).

Formula

a(n) = 81*5^(n-2) for n > 1.

G.f.: x*(4*x - 17)/(5*x - 1).

E.g.f.: (81*exp(5*x) + 20*x - 81)/25. - Stefano Spezia, Sep 04 2021

Mathematica

Join[{17}, LinearRecurrence[{5}, {81}, 20]]
CoefficientList[Series[(4 x - 17)/(5 x - 1), {x, 0, 20}], x]

Crossrefs

Cf. A180148, A228602, A347478.

Sequence in context: A100688 A044204 A044585 * A197397 A354012 A053826

Adjacent sequences: A347498 A347499 A347500 * A347502 A347503 A347504

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 04 2021

Status

approved