%I #19 Mar 15 2024 21:27:36

%S 0,0,0,0,24,252,1032,2836,6332,12496,22328,37020,58148,87520,127056,

%T 178868,245260,328728,431960,557836,709428,890000,1103008,1352100,

%U 1641116,1974088,2355240,2788988,3279940,3832896

%N Number of chordless cycles in the complement of the n X n antelope graph.

%C All cycles are of length 4.

%H Paolo Xausa, <a href="/A370110/b370110.txt">Table of n, a(n) for n = 1..10000</a>

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

%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/GraphComplement.html">Graph Complement</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = 2*(4*n^4-56*n^3+185*n^2+903*n-5142) for n > 11.

%F From _Chai Wah Wu_, Feb 10 2024: (Start)

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 16.

%F G.f.: x^5*(-80*x^11 + 120*x^10 + 152*x^9 - 192*x^8 - 168*x^7 + 284*x^6 - 112*x^5 - 72*x^4 + 44*x^3 - 12*x^2 - 132*x - 24)/(x - 1)^5. (End)

%t LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 0, 24, 252, 1032, 2836, 6332, 12496, 22328, 37020, 58148, 87520, 127056, 178868}, 50] (* _Paolo Xausa_, Mar 15 2024 *)

%o (Python)

%o def A370110(n): return (0, 0, 0, 0, 24, 252, 1032, 2836, 6332, 12496, 22328)[n-1] if n<12 else n*(n*(n*(4*n - 56) + 185) + 903) - 5142<<1 # _Chai Wah Wu_, Feb 10 2024

%K nonn,easy

%O 1,5

%A _Eric W. Weisstein_, Feb 10 2024