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

Author

Paul Curtz, Sep 30 2007

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A065423.

Programs

Magma

[(6*n^2-10*n+17-(1+2*n)*(-1)^n)/16: n in [0..70]]; // Vincenzo Librandi, Jul 29 2015

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 *)
Join[{1},Accumulate[LinearRecurrence[{0,2,0,-1},{0,0,2,1},100]]+1] (* Harvey P. Dale, May 28 2025 *)

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

Extensions

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