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 A303006 #16 Jun 10 2025 19:07:08
%S A303006 2,4,5,36,27,25,114,196,437,729,1674,3249,6450,12996,24870,49284,
%T A303006 95882,190969,369666,724201,1425261,2802276,5495162,10764961,21186827,
%U A303006 41602500,81686669,160326244,314946266,618516900,1214288106,2384368900,4681737021,9193357924
%N A303006 Number of minimal total dominating sets in the n-prism graph.
%C A303006 Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Apr 17 2018
%H A303006 Andrew Howroyd, <a href="/A303006/b303006.txt">Table of n, a(n) for n = 1..200</a>
%H A303006 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalTotalDominatingSet.html">Minimal Total Dominating Set</a>.
%H A303006 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>.
%H A303006 <a href="/index/Rec#order_32">Index entries for linear recurrences with constant coefficients</a>, signature (2, -2, 3, 4, -7, 5, 0, -21, 39, -24, 21, 33, -36, 63, -33, 0, 33, -63, 36, -33, -21, 24, -39, 21, 0, -5, 7, -4, -3, 2, -2, 1).
%F A303006 G.f.: x*(2 + x^2 + 28*x^3 - 55*x^4 + 26*x^5 + 8*x^6 - 192*x^7 + 359*x^8 - 180*x^9 + 83*x^10 + 552*x^11 - 700*x^12 + 906*x^13 - 583*x^14 - 228*x^15 + 605*x^16 - 1362*x^17 + 596*x^18 - 636*x^19 - 673*x^20 + 684*x^21 - 1045*x^22 + 564*x^23 + 8*x^24 - 154*x^25 + 197*x^26 - 116*x^27 - 107*x^28 + 72*x^29 - 70*x^30 + 36*x^31)/((1 - x)*(1 + x)*(1 - 2*x - x^2 + 3*x^3 - x^4 - 2*x^5 + x^6)*(1 - 4*x + 10*x^2 - 19*x^3 + 28*x^4 - 34*x^5 + 37*x^6 - 34*x^7 + 28*x^8 - 19*x^9 + 10*x^10 - 4*x^11 + x^12)*(1 + 4*x + 10*x^2 + 19*x^3 + 28*x^4 + 34*x^5 + 37*x^6 + 34*x^7 + 28*x^8 + 19*x^9 + 10*x^10 + 4*x^11 + x^12)). - _Andrew Howroyd_, Apr 17 2018
%t A303006 Table[3 + 3 (-1)^n + RootSum[1 - 2 # - #^2 + 3 #^3 - #^4 - 2 #^5 + #^6 &, #^n &] + RootSum[1 - 4 # + 10 #^2 - 19 #^3 + 28 #^4 - 34 #^5 + 37 #^6 - 34 #^7 + 28 #^8 - 19 #^9 + 10 #^10 - 4 #^11 + #^12 &, #^n &] + RootSum[1 + 4 # + 10 #^2 + 19 #^3 + 28 #^4 + 34 #^5 + 37 #^6 + 34 #^7 + 28 #^8 + 19 #^9 + 10 #^10 + 4 #^11 + #^12 &, #^n &], {n, 200}]
%t A303006 LinearRecurrence[{2, -2, 3, 4, -7, 5, 0, -21, 39, -24, 21, 33, -36,
%t A303006 63, -33, 0, 33, -63, 36, -33, -21, 24, -39, 21, 0, -5, 7, -4, -3,
%t A303006 2, -2, 1}, {2, 4, 5, 36, 27, 25, 114, 196, 437, 729, 1674, 3249,
%t A303006 6450, 12996, 24870, 49284, 95882, 190969, 369666, 724201, 1425261,
%t A303006 2802276, 5495162, 10764961, 21186827, 41602500, 81686669, 160326244, 314946266, 618516900, 1214288106, 2384368900}, 200]
%t A303006 CoefficientList[Series[(2 + x^2 + 28 x^3 - 55 x^4 + 26 x^5 + 8 x^6 - 192 x^7 + 359 x^8 - 180 x^9 + 83 x^10 + 552 x^11 - 700 x^12 + 906 x^13 - 583 x^14 - 228 x^15 + 605 x^16 - 1362 x^17 + 596 x^18 - 636 x^19 - 673 x^20 + 684 x^21 - 1045 x^22 + 564 x^23 + 8 x^24 - 154 x^25 + 197 x^26 - 116 x^27 - 107 x^28 + 72 x^29 - 70 x^30 + 36 x^31)/((1 - x) (1 + x) (1 - 2 x - x^2 + 3 x^3 - x^4 - 2 x^5 + x^6) (1 - 4 x + 10 x^2 - 19 x^3 + 28 x^4 - 34 x^5 + 37 x^6 - 34 x^7 + 28 x^8 - 19 x^9 + 10 x^10 - 4 x^11 + x^12) (1 + 4 x + 10 x^2 + 19 x^3 + 28 x^4 + 34 x^5 + 37 x^6 + 34 x^7 + 28 x^8 + 19 x^9 + 10 x^10 + 4 x^11 + x^12)), {x, 0, 199}], x]
%Y A303006 Cf. A290336, A296102, A302405, A303053.
%K A303006 nonn,easy
%O A303006 1,1
%A A303006 _Eric W. Weisstein_, Apr 17 2018
%E A303006 a(1)-a(2) and terms a(10) and beyond from _Andrew Howroyd_, Apr 17 2018