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Number of chordless cycles in the complement of the n-Sierpinski gasket graph.
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%I #7 Feb 14 2024 17:31:35

%S 0,0,171,2628,27495,259560,2372931,21467628,193542975,1742890320,

%T 15689024091,141210251028,1270919362455,11438355572280,

%U 102945444081651,926509728528828,8338589752141935,75047314355425440,675425848957273611,6078832699890797028,54709494476843177415

%N Number of chordless cycles in the complement of the n-Sierpinski gasket graph.

%C All complement chordless cycles are of length 4.

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

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

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27).

%F a(n) = (72-17*3^n+9^n)/2 for n > 1.

%F a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3) for n > 4.

%F G.f. -9*x^3*(19+45*x)/((-1+x)*(-1+3*x)*(-1+9*x)).

%t Join[{0}, Table[(72 - 17 3^n + 9^n)/2, {n, 2, 10}]]

%t Join[{0}, LinearRecurrence[{13, -39, 27}, {0, 171, 2628}, 20]]

%t CoefficientList[Series[-9 x^2 (19 + 45 x)/((-1 + x) (-1 + 3 x) (-1 + 9 x)), {x, 0, 20}], x]

%K nonn,easy

%O 1,3

%A _Eric W. Weisstein_, Feb 14 2024