A347503 - OEIS

%I #5 Feb 16 2025 08:34:02

%S 5,13,29,57,115,229,453,897,1775,3513,6957,13785,27331,54221,107629,

%T 213761,424767,844465,1679605,3342057,6652563,13247093,26387445,

%U 52578561,104796015,208927849,416634077,831021241,1657909763,3308218269,6602455645,13179196417

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

%C Sequence extended to a(1) using the formula/recurrence.

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

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,0,-1,2).

%F a(n)=4*a(n-1)-4*a(n-2)-a(n-4)+2*a(n-5).

%F G.f.: -x*(5-7*x-3*x^2-7*x^3+8*x^4)/((-1+x)*(-1+2*x)*(-1+x+x^2+x^3)).

%t Table[RootSum[-1 - # - #^2 + #^3 &, #^n &] + 3 2^n - 2, {n, 20}]

%t CoefficientList[Series[-(5 - 7 x - 3 x^2 - 7 x^3 + 8 x^4)/((-1 + x) (-1 + 2 x) (-1 + x + x^2 + x^3)), {x, 0, 20}], x]

%K nonn,changed

%O 1,1

%A _Eric W. Weisstein_, Sep 04 2021