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 A302255 #50 Feb 16 2025 08:33:53
%S A302255 0,1,2,2,3,4,4,4,5,6,6,7,8,8,8,9,10,10,11,12,12,12,13,14,14,15,16,16,
%T A302255 16,17,18,18,19,20,20,20,21,22,22,23,24,24,24,25,26,26,27,28,28,28,29,
%U A302255 30,30,31,32,32,32,33,34,34,35,36,36,36,37,38,38,39,40,40,40,41
%N A302255 Total domination number of the n-antiprism graph.
%C A302255 Sequence extended to a(0)-a(2) using the recurrence/formula.
%H A302255 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H A302255 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominationNumber.html">Total Domination Number</a>
%H A302255 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A302255 a(n) = a(n-1) + a(n-7) - a(n-8).
%F A302255 G.f.: x*(1 + x + x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
%F A302255 a(n) = a(n-7) + 4. - _Andrew Howroyd_, Apr 18 2018
%F A302255 a(n) = a(n-7*k) + 4*k. - _Eric W. Weisstein_, Apr 19 2018
%t A302255 Table[(4 + 4 n + E^(4 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 1] + E^(-4 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 2] + E^(-2 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 3] + E^(2 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 4] + E^(-6 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 5] + E^(6 I n Pi/7) Root[1 + 7 #^2 + 28 #^3 + 42 #^4 + 28 #^5 + 7 #^6 &, 6])/ 7, {n, 20}] // RootReduce
%t A302255 LinearRecurrence[{1,0,0,0,0,0,1,-1}, {1,2,2,3,4,4,4,5,6,6}, {0, 20}]
%t A302255 CoefficientList[Series[x (1 + x + x^3 + x^4)/((1 - x)^2 (1 + x + x^2 + x^3 + x^4 + x^5 + x^6)), {x, 0, 20}], x]
%o A302255 (PARI) x='x+O('x^50); concat(0, Vec(x*(1+x+x^3+x^4)/((1-x)^2*(1+x+x^2+ x^3+x^4+x^5+x^6)))) \\ _G. C. Greubel_, Apr 09 2018
%o A302255 (Magma) I:=[2,2,3,4,4,4,5,6]; [0,1] cat [n le 8 select I[n] else Self(n-1) + Self(n-7) - Self(n-8): n in [1..30]]; // _G. C. Greubel_, Apr 09 2018
%Y A302255 Cf. A302652, A302760, A302763.
%K A302255 nonn,easy
%O A302255 0,3
%A A302255 _Eric W. Weisstein_, Apr 07 2018