A297665 Number of chordless cycles in the n-web graph.

3, 10, 17, 26, 37, 54, 83, 132, 211, 336, 535, 856, 1377, 2222, 3589, 5798, 9369, 15146, 24495, 39624, 64103, 103708, 167787, 271468, 439229, 710674, 1149881, 1860530, 3010381, 4870878, 7881227, 12752076, 20633275, 33385320, 54018559, 87403840, 141422361, 228826166

Offset

3,1

Links

Table of n, a(n) for n=3..40.

Eric Weisstein's World of Mathematics, Chordless Cycle

Eric Weisstein's World of Mathematics, Web Graph

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, 0, -2, 1).

Formula

a(n) = A000032(n) + A057079(n+1) + n for n >= 4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 2*a(n-5) + a(n-6) for n >= 10.

G.f.: -x^3*(2*x^6 - 5*x^4 + 6*x^3 - 5*x^2 - 2*x + 3)/((x - 1)^2*(x^2 - x + 1)*(x^2 + x - 1)).

Mathematica

LinearRecurrence[{4, -6, 4, 0, -2, 1}, {3, 10, 17, 26, 37, 54, 83}, 38]

Crossrefs

A000032, A057079, A301775.

Sequence in context: A047702 A219726 A017017 * A309347 A273235 A334964

Adjacent sequences: A297662 A297663 A297664 * A297666 A297667 A297668

Keyword

nonn,easy

Author

Eric W. Weisstein, Jan 02 2018

Extensions

Terms for n >= 9 corrected, and formulas and programs adjusted by Pontus von Brömssen, Nov 13 2022

Status

approved