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A364273
Number of chordless cycles (with length >= 4) in the complement of the n X n X n grid graph.
0
0, 6, 780, 7992, 39339, 134754, 369918, 873000, 1844637, 3581154, 6501024, 11174568, 18356895, 29024082, 44412594, 66061944, 95860593, 136095090, 189502452, 259325784, 349373139, 464079618, 608572710, 788740872, 1011305349, 1283895234, 1615125768, 2014679880
OFFSET
1,2
COMMENTS
Chordless cycles are all of length 4.
LINKS
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Rook Complement Graph
FORMULA
a(n) = 3/2*(16-108*n+155*n^2-57*n^3+3*n^4-6*n^5+3*n^6) for n > 2.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) -35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 2.
G.f.: (-3*x^2*(2+246*x+886*x^2-145*x^3+41*x^4+71*x^5-25*x^6+4*x^7))/(-1+x)^7.
MATHEMATICA
Table[Piecewise[{{0, n == 1}, {6, n == 2}}, 3/2 (16 - 108 n + 155 n^2 - 57 n^3 + 3 n^4 - 6 n^5 + 3 n^6)], {n, 20}]
CoefficientList[Series[-((3 x (2 + 246 x + 886 x^2 - 145 x^3 + 41 x^4 + 71 x^5 - 25 x^6 + 4 x^7))/(-1 + x)^7), {x, 0, 20}], x]
Join[{0, 6}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {780, 7992, 39339, 134754, 369918, 873000, 1844637}, 18]]
CROSSREFS
Sequence in context: A332176 A088217 A242850 * A020542 A045480 A006114
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 17 2023
EXTENSIONS
a(9) from Eric W. Weisstein, Aug 02 2023
a(10) and beyond from Eric W. Weisstein, Aug 15-16 2023
STATUS
approved