OFFSET
3,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 3..6287
Natasha Morrison and Alex Scott, Maximizing the number of induced cycles in a graph, Preprint, 2016. See Cor. 1.3.
Natasha Morrison and Alex Scott, Maximising the number of induced cycles in a graph, Journal of Combinatorial Theory Series B 126 (2017), 24-61.
FORMULA
From Chai Wah Wu, Sep 11 2016: (Start)
a(n) = a(n-1) + 4*a(n-3) - 4*a(n-4) - 3*a(n-6) + 3*a(n-7) for n > 9.
a(n) = 4*a(n-3) - 3*a(n-6) - 72 for n > 8.
G.f.: x^3*(30*x^6 - 223*x^5 + 190*x^4 + 105*x^3 + 73*x^2 - 64*x - 39)/((x - 1)^2*(3*x^3 - 1)*(x^2 + x + 1)). (End)
MAPLE
f:=n-> if n mod 3 = 0 then 3^(n/3)+12*n
elif n mod 3 = 1 then 4*3^((n-4)/3)+12*n+51
else 2*3^((n-2)/3)+12*n-36; fi;
[seq(f(n), n=3..40)];
MATHEMATICA
CoefficientList[Series[(30 x^6 -223 x^5 + 190 x^4 + 105 x^3 + 73 x^2 - 64 x - 39) / ((x-1)^2 (3 x^3-1) (x^2+x+1)), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 12 2016 *)
Table[Which[Mod[n, 3]==0, 3^(n/3)+12n, Mod[n, 3]==1, 4*3^((n-4)/3)+12n+51, True, 2*3^((n-2)/3)+12n-36], {n, 3, 40}] (* Harvey P. Dale, Nov 16 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 11 2016
STATUS
approved