A347481 - OEIS

%I #15 Dec 24 2024 02:15:35

%S 4,10,25,54,104,205,410,814,1609,3190,6340,12609,25094,49990,99665,

%T 198814,396784,792205,1582210,3160854,6315929,12622510,25229900,

%U 50435329,100831054,201598030,403092385,806017014,1611762584,3223085965,6445461290,12889772734

%N Number of total 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="http://mathworld.wolfram.com/DipyramidalGraph.html">Dipyramidal Graph</a>

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,3,-2,-1,2).

%F a(n) = Lucas(n) + 2*cos(n*Pi/2) + 3*2^n - 3.

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

%F G.f.: -x*(4 - 6*x + 5*x^2 - 8*x^3 - 9*x^4 + 8*x^5)/((-1 + x)*(-1 + 2*x)*(1 + x^2)*(-1 + x + x^2)).

%t Table[LucasL[n] + 2 Cos[n Pi/2] + 3 2^n - 3, {n, 50}]

%t LinearRecurrence[{4, -5, 3, -2, -1, 2}, {4, 10, 25, 54, 104, 205}, 20]

%t CoefficientList[Series[-(4 - 6 x + 5 x^2 - 8 x^3 - 9 x^4 + 8 x^5)/((-1 + x) (-1 + 2 x) (1 + x^2) (-1 + x + x^2)), {x, 0, 20}], x]

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Sep 03 2021