OFFSET
0,4
COMMENTS
Number of 132-avoiding even Grassmannian permutations of size n. - Juan B. Gil, Mar 10 2023
LINKS
Juan B. Gil and Jessica A. Tomasko, Pattern-avoiding even and odd Grassmannian permutations, arXiv:2207.12617 [math.CO], 2022.
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
From R. J. Mathar, Jul 17 2009: (Start)
G.f.: (1 - 2*x^2 + 2*x^3 + 2*x^4)/((1+x)^2*(1-x)^3).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), n > 5. (End)
a(n) = (6*n^2 - 10*n + 17 - (1+2n)*(-1)^n)/16. - Wesley Ivan Hurt, Jul 28 2015
a(n) = 1 + binomial(n,2) - binomial(floor(n/2)+1,2). - Juan B. Gil, Mar 10 2023
MAPLE
A065423 := proc(n) if n mod 2 <> 0 then n-1 ; else n/2-1 ; fi ; end: A131355 := proc(n) 1+add(A065423(i), i=1..n) ; end: seq(A131355(n), n=0..80) ; # R. J. Mathar, Oct 04 2007
MATHEMATICA
Table[(6 n^2 - 10 n + 17 - (1 + 2 n) (-1)^n)/16, {n, 0, 100}] (* Wesley Ivan Hurt, Jul 28 2015 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 1, 1, 3, 4}, 70] (* Vincenzo Librandi, Jul 29 2015 *)
PROG
(Magma) [(6*n^2-10*n+17-(1+2*n)*(-1)^n)/16: n in [0..70]]; // Vincenzo Librandi, Jul 29 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Sep 30 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 04 2007
STATUS
approved