A367985 Number of 4-cycles in the n-cycle complement and (n+1)-wheel complement graph.

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

Table of n, a(n) for n=3..43.

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.

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

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

Adjacent sequences: A367982 A367983 A367984 * A367986 A367987 A367988

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 07 2023

Extensions

Name extended by Eric W. Weisstein, Dec 07 2023

Status

approved