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A248427
Circumference of the (n,n)-knight graph.
1
8, 14, 24, 36, 48, 64, 80, 100, 120, 144, 168, 196, 224, 256, 288, 324, 360, 400, 440, 484, 528, 576, 624, 676, 728, 784, 840, 900, 960, 1024, 1088, 1156, 1224, 1296, 1368, 1444, 1520, 1600, 1680, 1764, 1848, 1936, 2024, 2116, 2208, 2304, 2400, 2500, 2600, 2704, 2808, 2916, 3024, 3136, 3248, 3364
OFFSET
3,1
COMMENTS
Colin Barker's conjectures confirmed using first Mathematica program. - Ray Chandler, Jan 14 2024
LINKS
Eric Weisstein's World of Mathematics, Graph Circumference
Eric Weisstein's World of Mathematics, Knight Graph
FORMULA
From Colin Barker, Oct 07 2014: (Start)
a(n) = (-1+(-1)^n+2*n^2)/2 for n>4.
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>8.
G.f.: -2*x^3*(x^5-2*x^4+2*x^3-2*x^2-x+4) / ((x-1)^3*(x+1)).
(End)
MATHEMATICA
Table[Piecewise[{{14, n == 4}, {n^2, Mod[n, 2] == 0}, {n^2 - 1, Mod[n, 2] == 1}}], {n, 3, 50}]
CoefficientList[Series[-2x^3(x^5-2x^4+2x^3-2x^2-x+4)/((x-1)^3(x+1)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {8, 14, 24, 36, 48, 64}, 50] (* Harvey P. Dale, Jan 05 2024 *)
CROSSREFS
Sequence in context: A250098 A155156 A275898 * A090993 A211525 A241161
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Oct 06 2014
STATUS
approved