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

5,1

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).

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

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 *)

Crossrefs

Column k=2 of A238858.

Sequence in context: A219160 A111034 A214367 * A109801 A099340 A221605

Adjacent sequences: A241869 A241870 A241871 * A241873 A241874 A241875

Keyword

nonn,easy

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved