A364668 Domination and lower independence number of the n-Goldberg graph.

0, 3, 5, 7, 9, 11, 14, 16, 18, 20, 22, 25, 27, 29, 31, 33, 36, 38, 40, 42, 44, 47, 49, 51, 53, 55, 58, 60, 62, 64, 66, 69, 71, 73, 75, 77, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 102, 104, 106, 108, 110, 113, 115, 117, 119, 121, 124, 126, 128, 130, 132

Offset

0,2

Comments

The Goldberg graph is defined for n >= 3.

Extended to n = 0 through 2 using the formula/recurrence.

Disagrees with A195167(n) at n = 26, 31, 36, 41, ....

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Domination Number.

Eric Weisstein's World of Mathematics, Goldberg Graph.

Eric Weisstein's World of Mathematics, Lower Independence Number.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

a(n) = a(n-1) + a(n-5) - a(n-6).

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

a(n) = floor((11*n + 4)/5). - Andrew Howroyd, May 25 2025

Mathematica

Table[(11 n - Cos[2 n Pi/5] - Cos[4 n Pi/5] + Sqrt[1 + 2/Sqrt[5]] Sin[2 n Pi/5] + Sqrt[1 - 2/Sqrt[5]] Sin[4 n Pi/5] + 2)/5, {n, 0, 20}]
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 3, 5, 7, 9, 11}, 20]
CoefficientList[Series[x (3 + 2 x + 2 x^2 + 2 x^3 + 2 x^4)/((-1 + x)^2 (1 + x + x^2 + x^3 + x^4)), {x, 0, 20}], x]

Crossrefs

Cf. A382431.

Sequence in context: A195179 A033038 A195167 * A211218 A291839 A134917

Adjacent sequences: A364665 A364666 A364667 * A364669 A364670 A364671

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 01 2023

Extensions

Name extended by Eric W. Weisstein, Mar 10 2025

Status

approved