OFFSET
0,3
LINKS
G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European Journal of Combinatorics, 28, 2007, 1724-1741.
Index entries for linear recurrences with constant coefficients, signature (8,-20,16,-4).
FORMULA
a(n) = Sum_{k=0..n} k*A059576(n,k).
G.f.: z(1-z)/(1-4z+2z^2)^2. [Corrected by Georg Fischer, May 19 2019]
EXAMPLE
a(2)=7 because the 2-compositions of 2, written as (top row / bottom row), are (0 / 2), (1 / 1), (2 / 0), (1,0 / 0,1), (0,1 / 1,0), (1,1 / 0,0), (0,0 / 1,1) and the sum of the entries in the top rows is 0 + 1 + 2 + 1 + 0 +0 +1 + 1 + 1 + 0 + 0 = 7.
MAPLE
g := z*(1-z)/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 30): seq(coeff(gser, z, k), k = 0 .. 25);
MATHEMATICA
CoefficientList[Series[x(1-x)/(1-4x+2x^2)^2, {x, 0, 30}], x] (* Georg Fischer, May 19 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Oct 12 2010
STATUS
approved