A387373 - OEIS

%I #15 Sep 03 2025 04:20:24

%S 5,281,15949,905469,51427345,2920698969,165875085993,9420532825569,

%T 535019698383817,30385338406252141,1725672517842528533,

%U 98006005364525379169,5566048591606153424165,316112230152526972676369,17952941015049437421057421,1019600193685412853211945813,57906086478637532521174425681

%N Number of connected dominating sets in the n-Cameron graph.

%C The n-Cameron graph is defined for n >= 1. The sequence has been extended to a(0) using the recurrence. - _Andrew Howroyd_, Aug 31 2025

%H Andrew Howroyd, <a href="/A387373/b387373.txt">Table of n, a(n) for n = 0..200</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CameronGraph.html">Cameron Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedDominatingSet.html">Connected Dominating Set</a>.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (53,209,376,-673,71,-4479,2120,-428,320,16).

%F G.f.: (5 + 16*x + 11*x^2 - 437*x^3 + 1856*x^4 - 1403*x^5 + 5308*x^6 - 2044*x^7 + 656*x^8 - 368*x^9)/(1 - 53*x - 209*x^2 - 376*x^3 + 673*x^4 - 71*x^5 + 4479*x^6 - 2120*x^7 + 428*x^8 - 320*x^9 - 16*x^10). - _Andrew Howroyd_, Aug 31 2025

%F a(n) = 53*a(n-1)+209*a(n-2)+376*a(n-3)-673*a(n-4)+71*a(n-5)-4479*a(n-6)+2120*a(n-7)-428*a(n-8)+320*a(n-9)+16*a(n-10). - _Eric W. Weisstein_, Sep 03 2025

%t LinearRecurrence[{53, 209, 376, -673, 71, -4479, 2120, -428, 320, 16}, {281, 15949, 905469, 51427345, 2920698969, 165875085993, 9420532825569, 535019698383817, 30385338406252141, 1725672517842528533}, {0, 20}] (* _Eric W. Weisstein_, Sep 03 2025 *)

%t CoefficientList[Series[(-5 - 16 x - 11 x^2 + 437 x^3 - 1856 x^4 + 1403 x^5 - 5308 x^6 + 2044 x^7 - 656 x^8 + 368 x^9)/(-1 + 53 x + 209 x^2 + 376 x^3 - 673 x^4 + 71 x^5 - 4479 x^6 + 2120 x^7 - 428 x^8 + 320 x^9 + 16 x^10), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 03 2025 *)

%Y Cf. A387374, A387433.

%K nonn,easy

%O 0,1

%A _Eric W. Weisstein_, Aug 28 2025

%E a(0) prepended and a(4) onwards from _Andrew Howroyd_, Aug 31 2025