OFFSET
1,1
COMMENTS
For n > 5, also the number of chordless cycles (all of length 4) in the torus grid graph C_n square C_n.
LINKS
Eric Weisstein's World of Mathematics, Chordless Cycle
Eric Weisstein's World of Mathematics, Graph Complement
Eric Weisstein's World of Mathematics, Torus Grid Graph
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: 3*(7-15*x-15*x^2+7*x^3)/(-1+x)^5.
MATHEMATICA
Table[n^2 (2 n^2 - 23), {n, 20}]
LinearRecurrence[{5, -10, 10, -5, 1}, {-21, -60, -45, 144, 675}, 20]
CoefficientList[Series[3 (7 - 15 x - 15 x^2 + 7 x^3)/(-1 + x)^5, {x, 0, 20}], x]
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Eric W. Weisstein, Feb 10 2024
STATUS
approved