A370299 Number of chordless cycles in the complement of the n-Sierpinski gasket graph.

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

Table of n, a(n) for n=1..21.

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

Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

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

Adjacent sequences: A370296 A370297 A370298 * A370300 A370301 A370302

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 14 2024

Status

approved