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 A362750 #24 Feb 16 2025 08:34:05
%S A362750 4,16,79,336,1144,4351,17224,67936,267919,1063216,4233904,16882191,
%T A362750 67380304,269142736,1075602319,4299846976,17192621224,68752838911,
%U A362750 274965310744,1099740514416,4398645585679,17593754283616,70372850295904,281485727082511,1125928050595744
%N A362750 Number of total dominating sets in the n-double cone graph.
%C A362750 The n-double cone graph is defined for n >= 3. The sequence has been extended to n=1 using the formula/recurrence. - _Andrew Howroyd_, May 03 2023
%H A362750 Andrew Howroyd, <a href="/A362750/b362750.txt">Table of n, a(n) for n = 1..500</a>
%H A362750 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleConeGraph.html">Double Cone Graph</a>
%H A362750 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%H A362750 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,18,-24,-6,27,-15,13,-4).
%F A362750 From _Andrew Howroyd_, May 03 2023: (Start)
%F A362750 a(n) = A001638(n)^2 + 4^n - 1.
%F A362750 a(n) = (A000032(n) + 2*A056594(n))^2 + 4^n - 1.
%F A362750 a(2*n-1) = A302603(4*n-1).
%F A362750 a(n) = 7*a(n-1) - 15*a(n-2) + 18*a(n-3) - 24*a(n-4) - 6*a(n-5) + 27*a(n-6) - 15*a(n-7) + 13*a(n-8) - 4*a(n-9) for n > 9.
%F A362750 G.f.: x*(4 - 12*x + 27*x^2 - 49*x^3 - 215*x^4 + 369*x^5 - 237*x^6 + 207*x^7 - 64*x^8)/((1 - x)*(1 + x)*(1 - 4*x)*(1 - 3*x + x^2)*(1 + 3*x^2 + x^4)).
%F A362750 (End)
%t A362750 Table[1 + 4 (-1)^n + 4^n + LucasL[2 n] + 4 LucasL[n] Cos[n Pi/2], {n, 20}] (* _Eric W. Weisstein_, Sep 09 2023 *)
%t A362750 Table[(2 Cos[n Pi/2] + Fibonacci[n + 1] + Fibonacci[n - 1])^2 + 4^n - 1, {n, 20}] (* _Eric W. Weisstein_, Sep 09 2023 *)
%t A362750 LinearRecurrence[{7, -15, 18, -24, -6, 27, -15, 13, -4}, {4, 16, 79, 336, 1144, 4351, 17224, 67936, 267919}, 20] (* _Eric W. Weisstein_, Sep 09 2023 *)
%t A362750 CoefficientList[Series[4/(1 - 4 x) + 1/(1 - x) - 4/(1 + x) + (3 - 2 x)/(1 + (-3 + x) x) - 4 x (3 + 2 x^2)/(1 + 3 x^2 + x^4), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 09 2023 *)
%o A362750 (PARI) a(n) = {(fibonacci(n+1) + fibonacci(n-1) + I^n + (-I)^n)^2 + 4^n - 1} \\ _Andrew Howroyd_, May 03 2023
%Y A362750 Cf. A000032, A001638, A056594, A302603.
%K A362750 nonn,easy
%O A362750 1,1
%A A362750 _Eric W. Weisstein_, May 02 2023
%E A362750 a(1)-a(2) prepended and a(16) and beyond from _Andrew Howroyd_, May 03 2023