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approved

editing

proposed

allocated for Eric W. Weisstein

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

0,2

Extended to n = 0 using the formula/recurrence.

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

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldbergGraph.html">Goldberg Graph</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LowerIndependenceNumber.html">Lower Independence Number</a>

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

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)).

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]

allocated

nonn

Eric W. Weisstein, Aug 01 2023

approved

editing

allocated for Eric W. Weisstein

allocated

approved