A131355 Partial sums of A065423 plus one.

1, 1, 1, 3, 4, 8, 10, 16, 19, 27, 31, 41, 46, 58, 64, 78, 85, 101, 109, 127, 136, 156, 166, 188, 199, 223, 235, 261, 274, 302, 316, 346, 361, 393, 409, 443, 460, 496, 514, 552, 571, 611, 631, 673, 694, 738, 760, 806, 829, 877, 901, 951, 976, 1028, 1054, 1108

Offset

0,4

Comments

Number of 132-avoiding even Grassmannian permutations of size n. - Juan B. Gil, Mar 10 2023

Links

Table of n, a(n) for n=0..55.

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

Cf. A065423.

Sequence in context: A026494 A043306 A308844 * A092534 A005232 A165272

Adjacent sequences: A131352 A131353 A131354 * A131356 A131357 A131358

Keyword

nonn,easy

Author

Paul Curtz, Sep 30 2007

Extensions

More terms from R. J. Mathar, Oct 04 2007

Status

approved