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%I #11 Feb 25 2024 06:24:43
%S 1,6,9,12,15,22,35,56,87,134,209,332,533,858,1381,2224,3587,5794,9367,
%T 15148,24499,39626,64101,103704,167785,271470,439233,710676,1149879,
%U 1860526,3010379,4870880,7881231,12752078,20633273,33385316,54018557,87403842,141422365,228826168
%N Number of chordless cycles in the n-Moebius ladder.
%C Extended to a(1)-a(2) using the formula/recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, 0, -2, 1).
%F a(n) = n - 2*cos(n*Pi/3) + Lucas(n).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 2*a(n-5) + a(n-6).
%F G.f.: x*(-1 - 2*x + 9*x^2 - 8*x^3 + 3*x^4)/((-1+x)^2 *(x^2+x-1) *(x^2-x+1)).
%t Table[n - 2 Cos[n Pi/3] + LucasL[n], {n, 20}]
%t LinearRecurrence[{4, -6, 4, 0, -2, 1}, {1, 6, 9, 12, 15, 22}, 20]
%t CoefficientList[Series[(-1 - 2 x + 9 x^2 - 8 x^3 + 3 x^4)/((-1 + x)^2 (-1 + 2 x - x^2 + x^4)), {x, 0, 20}], x]
%o (PARI) x='x+O('x^23); Vec((-1 - 2*x + 9*x^2 - 8*x^3 + 3*x^4)/((-1 + x)^2* (-1 + 2*x - x^2 + x^4))) \\ _Georg Fischer_, Apr 03 2019
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Jan 02 2018
%E Terms a(1), a(2) prepended by _Georg Fischer_, Apr 03 2019