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 A382384 #17 Jun 04 2025 09:52:19
%S A382384 6,96,290,744,1974,5376,15642,45480,124014,343008,944658,2596776,
%T A382384 7116390,19409664,52694730,142812648,385840030,1039911520,2796034626,
%U A382384 7501233256,20084164374,53677896192,143214557050,381504047912,1014784646094,2695617288672,7151420301682
%N A382384 Number of minimum connected dominating sets in the n-Goldberg graph.
%C A382384 The connected domination number is given by 4*n - 1 = A004767(n - 1). - _Andrew Howroyd_, May 25 2025
%H A382384 Andrew Howroyd, <a href="/A382384/b382384.txt">Table of n, a(n) for n = 3..500</a>
%H A382384 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>.
%H A382384 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoldbergGraph.html">Goldberg Graph</a>.
%H A382384 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-16,-7,20,24,-64,97,236,-246,-368,7,252,-772,-64,1920,0,-1024).
%F A382384 G.f.: 2*x^3*(3 + 36*x - 53*x^2 - 256*x^3 - 2*x^4 + 592*x^5 + 1030*x^6 + 616*x^7 - 2817*x^8 - 2804*x^9 + 2591*x^10 + 2200*x^11 - 2592*x^12 - 2176*x^13 + 5168*x^14 + 3840*x^15 - 2304*x^16 - 2048*x^17)/((1 - x)*(1 + x)*(1 - x + 2*x^2)*(1 - x - 4*x^2)*(1 - x^2 - 4*x^3))^2. - _Andrew Howroyd_, May 25 2025
%t A382384 LinearRecurrence[{4, 2, -16, -7, 20, 24, -64, 97, 236, -246, -368, 7, 252, -772, -64, 1920, 0, -1024}, {6, 96, 290, 744, 1974, 5376, 15642, 45480, 124014, 343008, 944658, 2596776, 7116390, 19409664, 52694730, 142812648, 385840030, 1039911520}, 20] (* _Eric W. Weisstein_, Jun 04 2025 *)
%t A382384 CoefficientList[Series[2 (3 + 36 x - 53 x^2 - 256 x^3 - 2 x^4 + 592 x^5 + 1030 x^6 + 616 x^7 - 2817 x^8 - 2804 x^9 + 2591 x^10 + 2200 x^11 - 2592 x^12 - 2176 x^13 + 5168 x^14 + 3840 x^15 - 2304 x^16 - 2048 x^17)/((1 - x)^2 (1 + x)^2 (1 - x - 4 x^2)^2 (1 - x + 2 x^2)^2 (1 - x^2 - 4 x^3)^2), {x, 0, 20}], x] (* _Eric W. Weisstein_, Jun 04 2025 *)
%Y A382384 Cf. A004767, A382431.
%K A382384 nonn,easy
%O A382384 3,1
%A A382384 _Eric W. Weisstein_, Mar 23 2025
%E A382384 a(7) onwards from _Andrew Howroyd_, May 24 2025