A367993 Number of 4-cycles in the n X n white bishop graph.

0, 0, 6, 16, 50, 96, 196, 320, 540, 800, 1210, 1680, 2366, 3136, 4200, 5376, 6936, 8640, 10830, 13200, 16170, 19360, 23276, 27456, 32500, 37856, 44226, 50960, 58870, 67200, 76880, 87040, 98736, 110976, 124950, 139536, 156066, 173280, 192660

Offset

2,3

Links

Table of n, a(n) for n=2..40.

Eric Weisstein's World of Mathematics, Graph Cycle.

Eric Weisstein's World of Mathematics, White Bishop Graph.

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Formula

a(n) = (n - 1)^2*(2*n^2 - 4*n - 3 + 3*(-1)^n)/24.

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).

G.f.: -2*x^4*(3+2*x+3*x^2)/((-1+x)^5*(1+x)^3).

Mathematica

Table[(n - 1)^2 (2 n^2 - 4 n - 3 + 3 (-1)^n)/24, {n, 2, 20}]
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 0, 6, 16, 50, 96, 196, 320}, 20]
CoefficientList[Series[-2  x^2  (3 + 2  x + 3 x^2)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A364676 A341657 A288572 * A301978 A275585 A026086

Adjacent sequences: A367990 A367991 A367992 * A367994 A367995 A367996

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 07 2023

Status

approved