This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A284703 #23 Feb 16 2025 08:33:43
%S A284703 1,5,10,17,51,98,211,457,964,2095,4489,9638,20723,44469,95550,205225,
%T A284703 440777,946808,2033571,4367947,9381928,20151345,43283195,92967814,
%U A284703 199685501,428904403,921243124,1978737477,4250128177,9128846128,19607840133,42115660425
%N A284703 Number of maximal matchings in the n-prism graph.
%C A284703 Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, May 16 2017
%H A284703 Andrew Howroyd, <a href="/A284703/b284703.txt">Table of n, a(n) for n = 1..200</a>
%H A284703 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>
%H A284703 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal Independent Edge Set</a>
%H A284703 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>
%H A284703 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,2, 1,-1,2,1,-1,-1).
%F A284703 From _Andrew Howroyd_, May 16 2017 (Start)
%F A284703 a(n) = a(n-1)+2*a(n-2)+a(n-3)-a(n-4)+2*a(n-5)+a(n-6)-a(n-7)-a(n-8) for n>8.
%F A284703 G.f.: x*(-8*x^7-7*x^6+6*x^5+10*x^4 -4*x^3+3*x^2+4*x+1)/((x^2-x+1)*(x^3-x-1)*(x^3+2*x^2+x-1)).
%F A284703 (End)
%t A284703 LinearRecurrence[{1, 2, 1, -1, 2, 1, -1, -1}, {1, 5, 10, 17, 51, 98, 211, 457}, 40] (* _Vincenzo Librandi_, May 17 2017 *)
%t A284703 CoefficientList[Series[(-8 x^7 - 7 x^6 + 6 x^5 + 10 x^4 - 4 x^3 + 3 x^2 + 4 x + 1) / ((x^2 - x + 1) (x^3 - x - 1) (x^3 + 2 x^2 + x - 1)), {x, 0, 33}], x] (* _Vincenzo Librandi_, May 17 2017 *)
%t A284703 Table[2 Cos[n Pi/3] + RootSum[-1 - 2 # - #^2 + #^3 &, #^n &] +
%t A284703 RootSum[-1 + #^2 + #^3 &, #^n &], {n, 20}] (* _Eric W. Weisstein_, May 17 2017 *)
%o A284703 (PARI)
%o A284703 Vec((-8*x^7-7*x^6+6*x^5+10*x^4-4*x^3+3*x^2+4*x+1)/((x^2-x+1)*(x^3-x-1)*(x^3+2*x^2+x-1))+O(x^20)) \\ _Andrew Howroyd_, May 16 2017
%o A284703 (Magma) I:=[1,5,10,17,51,98,211,457]; [n le 8 select I[n] else Self(n-1)+2*Self(n-2)+Self(n-3)-Self(n-4)+2*Self(n-5)+Self(n-6)-Self(n-7)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, May 17 2017
%Y A284703 Cf. A284701, A286945, A284710, A102080, A068397, A123304.
%K A284703 nonn
%O A284703 1,2
%A A284703 _Eric W. Weisstein_, Apr 01 2017
%E A284703 a(1)-a(2) and a(20)-a(32) from _Andrew Howroyd_, May 16 2017