A301775 -id:A301775 - cp's OEIS frontend

A301774 Number of odd chordless cycles in the (2n+1)-prism graph.

2, 12, 30, 74, 200, 522, 1362, 3572, 9350, 24474, 64080, 167762, 439202, 1149852, 3010350, 7881194, 20633240, 54018522, 141422322, 370248452, 969323030, 2537720634, 6643838880, 17393796002, 45537549122, 119218851372, 312119004990, 817138163594, 2139295485800

Offset: 1

Eric W. Weisstein, Mar 26 2018

Sequence extended to a(1) using the formula/recurrence (actual count for the 3-prism is 0, which reproduces A301775).

Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (2, 1, 2, -1).

Cf. A002878, A131713, A301775.

Table[LucasL[2 n + 1] + 2 Cos[(2 n + 1) Pi/3], {n, 20}]
LinearRecurrence[{2, 1, 2, -1}, {2, 12, 30, 74}, 20]
CoefficientList[Series[-2 (-1 - 4 x - 2 x^2 + x^3)/(1 - 2 x - x^2 - 2 x^3 + x^4), {x, 0, 20}], x]

a(n) = A002878(n) + A131713(n).
a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4).
G.f.: -2*x*(1+x)*(x^2-3*x-1) / ( (1+x+x^2)*(x^2-3*x+1) ).

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

Original entry on oeis.org

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

Eric W. Weisstein, Jan 02 2018

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).

A000032, A057079, A301775.

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

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)).

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

cp's OEIS Frontend

A301774 Number of odd chordless cycles in the (2n+1)-prism graph.

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