OFFSET
4,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 4..1000
Pedro Fernando Fernández Espinosa and Agustín Moreno Cañadas, Homological Ideals as Integer Specializations of Some Brauer Configuration Algebras, arXiv:2104.00050 [math.RT], 2021.
FORMULA
G.f.: -x^4/((x-1)*(2*x-1)*(x+1)*(2*x^2-1)).
From Ridouane Oudra, Jul 13 2023: (Start)
a(n) = x/6 + ((-1)^n - 1)*y, where x = 2^n - 3*sqrt(2)^n + 2 and y = (1/2)*sqrt(2)^(n-1) - (1/4)*sqrt(2)^n - 1/6.
a(n) = ((3 - (-1)^n)/12)*(4^floor(n/2) - 3*2^floor(n/2) + 2).
a(2n) = (4^n)/6 - 2^(n-1) + 1/3.
a(2n+1) = 2*a(2n). (End)
EXAMPLE
a(6) = 7: 13|24|5|6, 15|24|3|6, 1|24|35|6, 15|26|3|4, 15|2|3|46, 1|26|35|4, 1|2|35|46.
a(7) = 14: 137|24|5|6, 13|24|57|6, 157|24|3|6, 15|24|37|6, 17|24|35|6, 1|24|357|6, 157|26|3|4, 15|26|37|4, 157|2|3|46, 15|2|37|46, 17|26|35|4, 1|26|357|4, 17|2|35|46, 1|2|357|46.
MATHEMATICA
Drop[CoefficientList[Series[-x^4/((x - 1) (2 x - 1) (x + 1) (2 x^2 - 1)), {x, 0, 36}], x], 4] (* Michael De Vlieger, Jun 15 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jul 09 2016
STATUS
approved