A181294 Number of 0's in all 2-compositions of n. 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.
0, 2, 10, 46, 198, 816, 3264, 12776, 49192, 186976, 703328, 2623072, 9712864, 35746816, 130873088, 476961920, 1731331200, 6262393344, 22580421120, 81188953600, 291176175104, 1041867493376, 3720118018048, 13257657264128
Offset: 0
Examples
a(2)=10 because the 2-compositions of 2, written as (top row / bottom row), are (1/1),(0/2),(2/0),(1,0/0,1),(0,1/1,0),(1,1/0,0),(0,0/1,1), having 0 + 1 + 1 + 2 + 2 + 2 + 2 = 10 zeros.
References
- 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.
Crossrefs
Cf. A181293
Programs
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Maple
g := 2*z*(1-z)^3/(1-4*z+2*z^2)^2: gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 0 .. 25);
Formula
G.f. = 2z(1-z)^3/(1-4z+2z^2)^2.
a(n) = 2*A181331(n). - Emeric Deutsch, Oct 13 2010
Comments