A241873 Number of ascent sequences of length n with exactly three descents.

1, 48, 822, 9305, 83590, 647891, 4537169, 29532566, 182034751, 1076357002, 6162251432, 34394051095, 188121970788, 1012370499109, 5376927101387, 28254655805724, 147182871736245, 761235618312420, 3914066453608570, 20027841005048805, 102071452026321906

Offset

6,2

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..1000

Index entries for linear recurrences with constant coefficients, signature (32,-461,3952,-22443,88896,-251663,512656,-745096,752672,-500976,196992,-34560).

Formula

G.f.: -(912*x^6-2440*x^5+2481*x^4-1177*x^3+253*x^2-16*x-1)*x^6 / ((5*x-1) *(4*x-1)^2 *(x-1)^2 *(3*x-1)^3 *(2*x-1)^4).

a(n) = 3*5^(n-1)/8 - 4^(n-1)*n/3 + 3^(n-2)*(6*n^2-2*n-7)/16 - 2^(n-5)*(n-2)*(n-1)*(n+3)/3 - n/24 + 1/16. - Vaclav Kotesovec, May 03 2014

Recurrence: a(n) = -34560*a(n-12) + 196992*a(n-11) - 500976*a(n-10) + 752672*a(n-9) - 745096*a(n-8) + 512656*a(n-7) - 251663*a(n-6) + 88896*a(n-5) - 22443*a(n-4) + 3952*a(n-3) - 461*a(n-2) + 32*a(n-1). - Fung Lam, May 05 2014

Maple

gf:= -(912*x^6-2440*x^5+2481*x^4-1177*x^3+253*x^2-16*x-1)*x^6/
      ((5*x-1)*(4*x-1)^2*(x-1)^2*(3*x-1)^3*(2*x-1)^4):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=6..30);

Mathematica

CoefficientList[Series[-(912 x^6 - 2440 x^5 + 2481 x^4 - 1177 x^3 + 253 x^2 - 16 x - 1)/((5 x - 1) (4 x - 1)^2 (x - 1)^2 (3 x - 1)^3 (2 x - 1)^4), {x, 0, 40}], x] (* Vincenzo Librandi, May 06 2014 *)
LinearRecurrence[{32, -461, 3952, -22443, 88896, -251663, 512656, -745096, 752672, -500976, 196992, -34560}, {1, 48, 822, 9305, 83590, 647891, 4537169, 29532566, 182034751, 1076357002, 6162251432, 34394051095}, 21] (* Ray Chandler, Jul 14 2015 *)

Crossrefs

Column k=3 of A238858.

Sequence in context: A350378 A192839 A014401 * A233784 A233959 A233177

Adjacent sequences: A241870 A241871 A241872 * A241874 A241875 A241876

Keyword

nonn,easy

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved