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A370299
Number of chordless cycles in the complement of the n-Sierpinski gasket graph.
0
0, 0, 171, 2628, 27495, 259560, 2372931, 21467628, 193542975, 1742890320, 15689024091, 141210251028, 1270919362455, 11438355572280, 102945444081651, 926509728528828, 8338589752141935, 75047314355425440, 675425848957273611, 6078832699890797028, 54709494476843177415
OFFSET
1,3
COMMENTS
All complement chordless cycles are of length 4.
LINKS
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Graph Complement
Eric Weisstein's World of Mathematics, Sierpinski Gasket Graph
FORMULA
a(n) = (72-17*3^n+9^n)/2 for n > 1.
a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3) for n > 4.
G.f. -9*x^3*(19+45*x)/((-1+x)*(-1+3*x)*(-1+9*x)).
MATHEMATICA
Join[{0}, Table[(72 - 17 3^n + 9^n)/2, {n, 2, 10}]]
Join[{0}, LinearRecurrence[{13, -39, 27}, {0, 171, 2628}, 20]]
CoefficientList[Series[-9 x^2 (19 + 45 x)/((-1 + x) (-1 + 3 x) (-1 + 9 x)), {x, 0, 20}], x]
CROSSREFS
Sequence in context: A186868 A185611 A195279 * A016058 A332418 A152926
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Feb 14 2024
STATUS
approved