%I #15 Apr 23 2018 14:28:33

%S 0,6,9,14,25,57,196,222,441,851,1936,3281,6084,12662,24964,48830,

%T 93636,188265,369664,725859,1423249,2798582,5503716,10790049,21206025,

%U 41601462,81703521,160396110,314991504,618413702,1214104336,2384319102,4681706929,9192838950

%N Number of minimal total dominating sets in the n-Moebius ladder.

%C Sequence extrapolated to n=1 using recurrence.

%H Andrew Howroyd, <a href="/A303162/b303162.txt">Table of n, a(n) for n = 1..200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</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_32">Index entries for linear recurrences with constant coefficients</a>, signature (2, -2, 3, 4, -7, 5, 0, -21, 39, -24, 21, 33, -36, 63, -33, 0, 33, -63, 36, -33, -21, 24, -39, 21, 0, -5, 7, -4, -3, 2, -2, 1).

%F G.f.: x^2*(6 - 3*x + 8*x^2 - 3*x^3 - 16*x^4 + 96*x^5 - 154*x^6 + 171*x^7 - 172*x^8 - 105*x^9 + 74*x^10 - 280*x^11 - 8*x^12 + 91*x^13 - 508*x^14 + 289*x^15 - 386*x^16 - 64*x^17 - 124*x^18 - 231*x^19 - 28*x^20 - 63*x^21 - 28*x^22 + 96*x^23 - 46*x^24 + 39*x^25 - 16*x^26 - 21*x^27 + 18*x^28 - 12*x^29 + 6*x^30)/((1 - x)*(1 + x)*(1 - 2*x - x^2 + 3*x^3 - x^4 - 2*x^5 + x^6)*(1 - 4*x + 10*x^2 - 19*x^3 + 28*x^4 - 34*x^5 + 37*x^6 - 34*x^7 + 28*x^8 - 19*x^9 + 10*x^10 - 4*x^11 + x^12)*(1 + 4*x + 10*x^2 + 19*x^3 + 28*x^4 + 34*x^5 + 37*x^6 + 34*x^7 + 28*x^8 + 19*x^9 + 10*x^10 + 4*x^11 + x^12)). - _Andrew Howroyd_, Apr 19 2018

%t Table[3 - 3 (-1)^n + RootSum[1 - 2 # - #^2 + 3 #^3 - #^4 - 2 #^5 + #^6 &, #^n &] - RootSum[1 - 4 # + 10 #^2 - 19 #^3 + 28 #^4 - 34 #^5 + 37 #^6 - 34 #^7 + 28 #^8 - 19 #^9 + 10 #^10 - 4 #^11 + #^12 &, #^n &] + RootSum[1 + 4 # + 10 #^2 + 19 #^3 + 28 #^4 + 34 #^5 + 37 #^6 + 34 #^7 + 28 #^8 + 19 #^9 + 10 #^10 + 4 #^11 + #^12 &, #^n &], {n, 200}]

%t LinearRecurrence[{2, -2, 3, 4, -7, 5, 0, -21, 39, -24, 21, 33, -36,

%t 63, -33, 0, 33, -63, 36, -33, -21, 24, -39, 21, 0, -5, 7, -4, -3,

%t 2, -2, 1}, {0, 6, 9, 14, 25, 57, 196, 222, 441, 851, 1936, 3281,

%t 6084, 12662, 24964, 48830, 93636, 188265, 369664, 725859, 1423249,

%t 2798582, 5503716, 10790049, 21206025, 41601462, 81703521, 160396110,314991504, 618413702, 1214104336, 2384319102}, 200]

%t Rest @ CoefficientList[Series[x^2 (6 - 3 x + 8 x^2 - 3 x^3 - 16 x^4 + 96 x^5 - 154 x^6 + 171 x^7 - 172 x^8 - 105 x^9 + 74 x^10 - 280 x^11 - 8 x^12 + 91 x^13 - 508 x^14 + 289 x^15 - 386 x^16 - 64 x^17 - 124 x^18 - 231 x^19 - 28 x^20 - 63 x^21 - 28 x^22 + 96 x^23 - 46 x^24 + 39 x^25 - 16 x^26 - 21 x^27 + 18 x^28 - 12 x^29 + 6 x^30)/((1 - x) (1 + x) (1 - 2 x - x^2 + 3 x^3 - x^4 - 2 x^5 + x^6) (1 - 4 x + 10 x^2 - 19 x^3 + 28 x^4 - 34 x^5 + 37 x^6 - 34 x^7 + 28 x^8 - 19 x^9 + 10 x^10 - 4 x^11 + x^12) (1 + 4 x + 10 x^2 + 19 x^3 + 28 x^4 + 34 x^5 + 37 x^6 + 34 x^7 + 28 x^8 + 19 x^9 + 10 x^10 + 4 x^11 + x^12)), {x, 0, 200}], x]

%Y Cf. A284663, A290337, A295420, A303006, A303046.

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Apr 19 2018

%E a(1)-a(2) and terms a(11) and beyond from _Andrew Howroyd_, Apr 19 2018