OFFSET
0,3
COMMENTS
Also, number of 2-compositions of n that have no odd entries in the top row.
A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
From Sean A. Irvine, Jun 05 2025: (Start)
Also, for n>=1 the number of walks of length n-1 starting at vertex 1 in the graph:
1-2
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4-3. (End)
LINKS
G. Castiglione, A. Frosini, E. Munarini, A. Restivo and S. Rinaldi, Combinatorial aspects of L-convex polyominoes, European J. Combin. 28 (2007), no. 6, 1724-1741.
Sean A. Irvine, Walks on Graphs.
Index entries for linear recurrences with constant coefficients, signature (2,2,-2).
FORMULA
G.f.: (1+z)*(1-z)^2/(1-2*z-2*z^2+2*z^3).
a(n) = A181304(n,0).
a(0)=1, a(1)=1, a(2)=3, a(3)=7, a(n)=2*a(n-1)+2*a(n-2)-2*a(n-3). - Harvey P. Dale, Mar 07 2012
EXAMPLE
a(2) = 3 because we have (1/1), (2/0), and (1,1/0,0) (the 2-compositions are written as (top row / bottom row)).
Alternatively, a(2) = 3 because we have (0/2), (2,0), and (0,0/1,1) (the 2-compositions are written as (top row/bottom row)).
MAPLE
g := (1+z)*(1-z)^2/(1-2*z-2*z^2+2*z^3): gser := series(g, z = 0, 35): seq(coeff(gser, z, n), n = 0 .. 32);
MATHEMATICA
CoefficientList[Series[((1+x)(1-x)^2)/(1-2x-2x^2+2x^3), {x, 0, 30}], x] (* or *) Join[{1}, LinearRecurrence[{2, 2, -2}, {1, 3, 7}, 30]] (* Harvey P. Dale, Mar 07 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Oct 13 2010
EXTENSIONS
Edited by N. J. A. Sloane, Oct 15 2010
STATUS
approved