A364668 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

Extended to n = 0 using the formula/recurrence.

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

Links

Table of n, a(n) for n=0..60.

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)).

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

Sequence in context: A195179 A033038 A195167 * A211218 A291839 A134917

Adjacent sequences: A364665 A364666 A364667 * A364669 A364670 A364671

Keyword

nonn

Author

Eric W. Weisstein, Aug 01 2023

Status

approved