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A367985
Number of 4-cycles in the n-cycle complement and (n+1)-wheel complement graph.
0
0, 0, 0, 3, 14, 42, 99, 200, 363, 609, 962, 1449, 2100, 2948, 4029, 5382, 7049, 9075, 11508, 14399, 17802, 21774, 26375, 31668, 37719, 44597, 52374, 61125, 70928, 81864, 94017, 107474, 122325, 138663, 156584, 176187, 197574, 220850, 246123, 273504, 303107
OFFSET
3,4
LINKS
Eric Weisstein's World of Mathematics, Cycle Complement Graph.
Eric Weisstein's World of Mathematics, Graph Cycle.
Eric Weisstein's World of Mathematics, Wheel Complement Graph.
FORMULA
a(n) = (n - 5)*n*(n^2 - 9*n + 22)/8 for n >= 5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n >= 5.
G.f.: x^6*(-3+x-2*x^2+x^3)/(-1+x)^5.
MATHEMATICA
Join[{0, 0}, Table[(n - 5) n (n^2 - 9 n + 22)/8, {n, 5, 20}]
Join[{0, 0}, LinearRecurrence[{5, -10, 10, -5, 1}, {0, 3, 14, 42, 99}, 20]]
CoefficientList[Series[x^3 (-3 + x - 2 x^2 + x^3)/(-1 + x)^5, {x, 0, 20}], x]
CROSSREFS
Sequence in context: A296267 A104905 A055650 * A000550 A124650 A291138
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 07 2023
EXTENSIONS
Name extended by Eric W. Weisstein, Dec 07 2023
STATUS
approved