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

Author

Eric W. Weisstein, Jan 02 2018

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

A000032, A057079, A301775.

Programs

Mathematica

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

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)).

Extensions

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