A297665 - OEIS

%I #9 Feb 16 2025 08:33:52

%S 3,10,17,26,37,54,83,132,211,336,535,856,1377,2222,3589,5798,9369,

%T 15146,24495,39624,64103,103708,167787,271468,439229,710674,1149881,

%U 1860530,3010381,4870878,7881227,12752076,20633275,33385320,54018559,87403840,141422361,228826166

%N Number of chordless cycles in the n-web graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChordlessCycle.html">Chordless Cycle</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WebGraph.html">Web Graph</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, 0, -2, 1).

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

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

%F 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)).

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

%Y A000032, A057079, A301775.

%K nonn,easy,changed

%O 3,1

%A _Eric W. Weisstein_, Jan 02 2018

%E Terms for n >= 9 corrected, and formulas and programs adjusted by _Pontus von Brömssen_, Nov 13 2022