A241872 Number of ascent sequences of length n with exactly two descents.

4, 53, 429, 2748, 15342, 78339, 376159, 1728458, 7689744, 33393393, 142376385, 598555320, 2489143090, 10264270175, 42048021027, 171366151974, 695585112660, 2814484154445, 11359684937605, 45759869226260, 184050366838134, 739376299832763, 2967455421451239

Offset: 5

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Keywords

• nonn
• easy

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-121,467,-1054,1388,-984,288).

Crossrefs

Column k=2 of A238858.

Programs

Maple

gf := -(12*x^2-15*x+4)*x^5/((4*x-1)*(x-1)*(3*x-1)^2*(2*x-1)^3):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=5..30);

Mathematica

CoefficientList[Series[-(12 x^2 - 15 x + 4)/((4 x - 1) (x - 1) (3 x - 1)^2 (2 x - 1)^3), {x, 0, 40}], x] (* Vincenzo Librandi, May 06 2014 *)
LinearRecurrence[{17,-121,467,-1054,1388,-984,288},{4,53,429,2748,15342,78339,376159},23] (* Ray Chandler, Jul 14 2015 *)

Formula

G.f.: -(12*x^2-15*x+4)*x^5/((4*x-1)*(x-1)*(3*x-1)^2*(2*x-1)^3).

a(n) = 4^n/6 - 3^(n-1)*(2*n+1)/4 + 2^(n-4)*(n+2)*(n-1) + 1/12. - Vaclav Kotesovec, May 03 2014

Recurrence: a(n) = 288*a(n-7) - 984*a(n-6) + 1388*a(n-5) - 1054*a(n-4) + 467*a(n-3) - 121*a(n-2) + 17*a(n-1). - Fung Lam, May 05 2014