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 A303053 #24 Jun 09 2025 22:40:54
%S A303053 2,4,3,36,25,9,14,64,3,625,99,9,26,196,3,3136,221,9,38,400,3,9801,391,
%T A303053 9,50,676,3,23716,609,9,62,1024,3,48841,875,9,74,1444,3,90000,1189,9,
%U A303053 86,1936,3,152881,1551,9,98,2500,3,244036,1961,9,110,3136,3,370881
%N A303053 Number of minimum total dominating sets in the n-prism graph.
%C A303053 Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Apr 17 2018
%H A303053 Andrew Howroyd, <a href="/A303053/b303053.txt">Table of n, a(n) for n = 1..200</a>
%H A303053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumTotalDominatingSet.html">Minimum Total Dominating Set</a>.
%H A303053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>.
%H A303053 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,5,0,0,0,0,0,-10,0,0,0,0,0,10,0,0,0,0,0,-5,0,0,0,0,0,1).
%F A303053 From _Andrew Howroyd_, Apr 17 2018: (Start)
%F A303053 a(n) = 5*a(n-6) - 10*a(n-12) + 10*a(n-18) - 5*a(n-24) + a(n-30) for n > 30.
%F A303053 a(6*k) = 9, a(6*k+1) = 2*(6*k+1), a(6*k+2) = (6*k+2)^2, a(6*k+3) = 3, a(6*k+4) = ((2*k + 3)*(3*k + 2))^2, a(6*k+5) = (4*k + 5)*(6*k + 5). (End)
%t A303053 Table[(432 + 132 n + 85 n^2 + 10 n^3 + n^4 + (216 - 132 n + 37 n^2 + 10 n^3 + n^4) (-1)^n +(432 + 132 n - 37 n^2 - 10 n^3 - n^4) Cos[n Pi/3] + (864 - 132 n - 85 n^2 - 10 n^3 - n^4) Cos[2 n Pi/3] +Sqrt[3] (12 n - 13 n^2 - 10 n^3 - n^4) Sin[n Pi/3] + Sqrt[3] (12 n - 35 n^2 + 10 n^3 + n^4) Sin[2 n Pi/3])/216, {n, 200}]
%t A303053 Table[Piecewise[{{9, Mod[n, 6] == 0}, {2 n, Mod[n, 6] == 1}, {n^2, Mod[n, 6] == 2}, {3, Mod[n, 6] == 3}, {n^2 (n + 5)^2/36, Mod[n, 6] == 4}, {n (2 n + 5)/3, Mod[n, 6] == 5}}], {n, 200}]
%t A303053 LinearRecurrence[{0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 1}, {2, 4, 3, 36, 25, 9, 14, 64, 3, 625, 99, 9, 26, 196, 3, 3136, 221, 9, 38, 400, 3, 9801, 391, 9, 50, 676, 3, 23716, 609, 9}, 200]
%t A303053 Rest @ CoefficientList[Series[(9 x^6)/(1 - x^6) - (3 x^3)/(-1 + x^6) + (2 x (1 + 5 x^6))/(-1 + x^6)^2 + (x^5 (-25 - 24 x^6 + x^12))/(-1 + x^6)^3 - (4 x^2 (1 + 13 x^6 + 4 x^12))/(-1 + x^6)^3 - (x^4 (36 + 445 x^6 + 371 x^12 + 11 x^18 + x^24))/(-1 + x^6)^5, {x, 0, 200}], x]
%Y A303053 Cf. A296102, A302405, A303006.
%K A303053 nonn,easy
%O A303053 1,1
%A A303053 _Eric W. Weisstein_, Apr 17 2018
%E A303053 a(1)-a(2) and terms a(15) and beyond from _Andrew Howroyd_, Apr 17 2018