A268598 Expansion of x^5*(4 - 5*x)/(1 - 2*x)^4.

0, 0, 0, 0, 0, 4, 27, 120, 440, 1440, 4368, 12544, 34560, 92160, 239360, 608256, 1517568, 3727360, 9031680, 21626880, 51249152, 120324096, 280166400, 647495680, 1486356480, 3391094784, 7693402112, 17364418560, 39007027200, 87241523200, 194330492928

Offset: 0

Author

Ran Pan, Feb 08 2016

Keywords

• nonn
• easy

Comments

a(n) is the number of North-East lattice paths from (0,0) to (n,n) that have exactly two east steps below y = x - 1 and exactly one east step above y = x+1. Details can be found in Section 4.1 in Pan and Remmel's link.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Ran Pan, Jeffrey B. Remmel, Paired patterns in lattice paths, arXiv:1601.07988 [math.CO], 2016.
• Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Crossrefs

Cf. A268462, A268586, A268587.

Programs

PARI

concat(vector(5), Vec((4-5*x)*x^5/(1-2*x)^4 + O(x^40))) \\ Michel Marcus, Feb 08 2016

Formula

G.f.: x^5*(4 - 5*x)/(1 - 2*x)^4.

From Colin Barker, Feb 08 2016: (Start)

a(n) = 2^(n-7)*(n-4)*(n-3)*(n+3) for n>2.

a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4) for n>3. (End)