cp's OEIS Frontend

A289143 Matching number of the n-triangular honeycomb acute knight graph.

%I A289143 #17 Feb 16 2025 08:33:48
%S A289143 0,0,3,3,6,9,12,18,21,27,33,39,45,51,60,67,75,84,94,105,114,126,138,
%T A289143 150,162,174,189,202,216,231,247,264,279,297,315,333,351,369,390,409,
%U A289143 429,450,472,495,516,540,564,588,612,636,663,688,714,741,769,798,825,855,885,915,945,975,1008,1039,1071,1104,1138,1173,1206,1242,1278,1314
%N A289143 Matching number of the n-triangular honeycomb acute knight graph.
%H A289143 Colin Barker, <a href="/A289143/b289143.txt">Table of n, a(n) for n = 1..1000</a>
%H A289143 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>
%H A289143 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MatchingNumber.html">Matching Number</a>
%H A289143 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumIndependentEdgeSet.html">Maximum Independent Edge Set</a>
%H A289143 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,-1,3,-3,1).
%F A289143 For n > 13, a(n) = (n^2-n+6-2*a(n-6))/2.
%F A289143 From _Colin Barker_, Jun 26 2017: (Start)
%F A289143 G.f.: x^3*(3 - 6*x + 6*x^2 - 3*x^3 + 3*x^5 - 3*x^6 + 3*x^8 - 3*x^9 + 3*x^11 - 3*x^12 + x^13) / ((1 - x)^3*(1 + x^2)*(1 - x^2 + x^4)).
%F A289143 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-6) + 3*a(n-7) - 3*a(n-8) + a(n-9) for n>9.
%F A289143 (End)
%t A289143 Table[Piecewise[{{3, n == 4}, {12, n == 7}}, (3 (n^2 + n - 3) + 5 Cos[n Pi/2] + 4 (-1)^n (Cos[n Pi/3] + Sqrt[3] Sin[n Pi/3]) (Cos[n Pi/2] - Sin[n Pi/2]) - 5 Sin[n Pi/2])/12], {n, 50}]
%o A289143 (PARI) concat(vector(2), Vec( x^3*(3 - 6*x + 6*x^2 - 3*x^3 + 3*x^5 - 3*x^6 + 3*x^8 - 3*x^9 + 3*x^11 - 3*x^12 + x^13) / ((1 - x)^3*(1 + x^2)*(1 - x^2 + x^4)) + O(x^80))) \\ _Colin Barker_, Jun 26 2017
%K A289143 nonn,easy
%O A289143 1,3
%A A289143 _Eric W. Weisstein_, Jun 26 2017