A381193 - OEIS

%I #19 Mar 03 2025 05:18:07

%S 5,6,12,33,77,153,274,460,741,1160,1776,2667,3933,5699,8118,11374,

%T 15685,21306,28532,37701,49197,63453,80954,102240,127909,158620,

%U 195096,238127,288573,347367,415518,494114,584325,687406,804700,937641,1087757,1256673,1446114

%N a(n) = (3*n-1)*(n^4-18*n^3+179*n^2-582*n+720)/120.

%C For n > 2, a(n) is the number of connected minimal dominating sets in the n-Andrasfai graph.

%H Vincenzo Librandi, <a href="/A381193/b381193.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).

%F G.f.: x*(5-24*x+51*x^2-49*x^3+14*x^4+6*x^5)/(-1+x)^6.

%F E.g.f.: 6 + exp(x)*(x^5/40 - 5*x^4/24 + 5*x^3/2 - 5*x^2 + 11*x - 6). - _Stefano Spezia_, Feb 17 2025

%t Table[(3 n - 1) (n^4 - 18 n^3 + 179 n^2 - 582 n + 720)/120, {n, 20}]

%t LinearRecurrence[{6, -15, 20, -15, 6, -1}, {5, 6, 12, 33, 77, 153}, 20]

%t CoefficientList[Series[(5 - 24 x + 51 x^2 - 49 x^3 + 14 x^4 + 6 x^5)/(-1 + x)^6, {x, 0, 20}], x]

%o (Python)

%o def A381193(n): return n*(n*(n*(n*(3*n - 55) + 555) - 1925) + 2742)//120-6 # _Chai Wah Wu_, Feb 16 2025

%o (Magma) [(3*n-1)*(n^4-18*n^3+179*n^2-582*n+720)/120: n in [1..50]]; // _Vincenzo Librandi_, Mar 03 2025

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Feb 16 2025