A370110 Number of chordless cycles in the complement of the n X n antelope graph.

0, 0, 0, 0, 24, 252, 1032, 2836, 6332, 12496, 22328, 37020, 58148, 87520, 127056, 178868, 245260, 328728, 431960, 557836, 709428, 890000, 1103008, 1352100, 1641116, 1974088, 2355240, 2788988, 3279940, 3832896

Offset

1,5

Comments

All cycles are of length 4.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Antelope Graph

Eric Weisstein's World of Mathematics, Chordless Cycle

Eric Weisstein's World of Mathematics, Graph Complement

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

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

From Chai Wah Wu, Feb 10 2024: (Start)

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

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)

Mathematica

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 *)

Prog

(Python)
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

Crossrefs

Sequence in context: A296648 A265858 A282859 * A000594 A278577 A022716

Adjacent sequences: A370107 A370108 A370109 * A370111 A370112 A370113

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 10 2024

Status

approved