%I #13 Mar 04 2024 00:09:37
%S 2,2,3,7,9,13,19,24,39,63,87,124,183,272,405,593,867,1261,1869,2760,
%T 4046,5936,8712,12817,18861,27720,40711,59792,87915,129250,189946,
%U 279118,410135,602803,886008,1302157,1913622,2812220,4133091,6074385,8927330,13119959
%N Number of maximal irredundant sets in the n-pan graph.
%C Sequence extended to a(1)-a(2) using the formula/recurrence. - _Andrew Howroyd_, Aug 23 2017
%H Andrew Howroyd, <a href="/A291102/b291102.txt">Table of n, a(n) for n = 1..500</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIrredundantSet.html">Maximal Irredundant Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PanGraph.html">Pan Graph</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, 1, 0, -1, -2, -1, 2, 1, 0, 0, -1).
%F From _Andrew Howroyd_, Aug 23 2017: (Start)
%F a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) - a(n-7) - 2*a(n-8) - a(n-9) + 2*a(n-10) + a(n-11) - a(n-14) for n > 14.
%F G.f.: x*(2 + 2*x + x^2 + 3*x^3 + 2*x^4 - x^5 - 2*x^6 - 6*x^7 - 3*x^8 + 7*x^9 + 3*x^10 - x^11 - 4*x^13)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2*x^8 + x^9 - 2*x^10 - x^11 + x^14).
%F (End)
%t Table[-RootSum[1 - #^3 - 2 #^4 + #^5 + 2 #^6 + #^7 - #^9 - #^10 - #^11 - #^12 + #^14 &, 500851004670498 #^(n+1) - 3689002954543242 #^(n+2) - 4674357321032747 #^(n+3) - 11682114439256677 #^(n+4) + 4235991226348286 #^(n+5) + 7038537508218316 #^(n+6) + 7181640141870472 #^(n+7) + 1546373234795414 #^(n+8) - 8648457478830123 #^(n+9) - 8135065519248445 #^(n+10) - 4540890555566032 #^(n+11) - 5314826024895471 #^(n+12) - 1546564184442276 #^(n+13) + 6933486092556085 #^(n+14) &]/47617929706047629, {n, 20}]
%t LinearRecurrence[{0, 1, 1, 1, 1, 0, -1, -2, -1, 2, 1, 0, 0, -1}, {2, 2, 3, 7, 9, 13, 19, 24, 39, 63, 87, 124, 183, 272}, 20]
%t CoefficientList[Series[(2 + 2 x + x^2 + 3 x^3 + 2 x^4 - x^5 - 2 x^6 - 6 x^7 - 3 x^8 + 7 x^9 + 3 x^10 - x^11 - 4 x^13)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2 x^8 + x^9 - 2 x^10 - x^11 + x^14), {x, 0, 20}], x]
%o (PARI) Vec((2 + 2*x + x^2 + 3*x^3 + 2*x^4 - x^5 - 2*x^6 - 6*x^7 - 3*x^8 + 7*x^9 + 3*x^10 - x^11 - 4*x^13)/(1 - x^2 - x^3 - x^4 - x^5 + x^7 + 2*x^8 + x^9 - 2*x^10 - x^11 + x^14)+O(x^40)) \\ _Andrew Howroyd_, Aug 23 2017
%Y Cf. A286954, A291107.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Aug 17 2017
%E a(1)-a(2) and terms a(21) and beyond from _Andrew Howroyd_, Aug 23 2017