A099235 A quadrisection of 1/(1-x-x^5).

1, 1, 5, 15, 45, 140, 431, 1326, 4085, 12580, 38740, 119305, 367411, 1131476, 3484490, 10730820, 33046585, 101770120, 313410816, 965178576, 2972359720, 9153665985, 28189589705, 86812537085, 267347509271, 823322219501

Offset: 0

Author

Paul Barry, Oct 08 2004

Keywords

• easy
• nonn

Comments

A row of A099233.

The number of ways to place non-overlapping Young diagrams of shape (2,1,1,1) on an 7 by n rectangle. - Per Alexandersson, Jun 23 2025

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,6,4,1).

Crossrefs

Cf. A003520, A099233.

Programs

Mathematica

Take[CoefficientList[Series[1/(1-x-x^5),{x,0,100}],x],{1,-1,4}] (* or *) LinearRecurrence[{1,4,6,4,1},{1,1,5,15,45},30] (* Harvey P. Dale, Mar 06 2015 *)

Formula

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

a(n) = Sum_{k=0..n} binomial(4(n-k), k).

a(n) = a(n-1) + 4*a(n-2) + 6*a(n-3) + 4*a(n-4) + a(n-5).

a(n) = A003520(4n).