%I #4 Aug 01 2023 17:02:48
%S 0,3,5,7,9,11,14,16,18,20,22,25,27,29,31,33,36,38,40,42,44,47,49,51,
%T 53,55,58,60,62,64,66,69,71,73,75,77,80,82,84,86,88,91,93,95,97,99,
%U 102,104,106,108,110,113,115,117,119,121,124,126,128,130,132
%N Lower independence number of the n-Goldberg graph.
%C Extended to n = 0 using the formula/recurrence.
%C Disagrees with A195167(n) at n = 26, 31, 36, 41, ....
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbergGraph.html">Goldberg Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LowerIndependenceNumber.html">Lower Independence Number</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F a(n) = a(n-1) + a(n-5) - a(n-6).
%F 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)).
%t 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}]
%t LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 3, 5, 7, 9, 11}, 20]
%t 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]
%K nonn
%O 0,2
%A _Eric W. Weisstein_, Aug 01 2023