A181339 Largest entry in a 2-composition of n, summed over 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.
2, 9, 38, 149, 562, 2066, 7474, 26737, 94900, 334909, 1176842, 4121632, 14397370, 50185498, 174628420, 606755258, 2105552976, 7298685677, 25275876584, 87457546835, 302382185770, 1044756677132, 3607460520006, 12449135054480
Offset: 1
Keywords
Examples
a(2)=9 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) and we have 1 + 2 + 2 + 1 + 1 + 1 + 1 = 9.
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. A181338
Programs
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Maple
h := proc (k) options operator, arrow: (1-z)^2/(1-4*z+2*z^2+2*z^(k+1)-z^(2*k+2)) end proc: f := proc (k) options operator, arrow: simplify(h(k)-h(k-1)) end proc: g := sum(k*f(k), k = 1 .. 50): gser := series(g, z = 0, 30): seq(coeff(gser, z, n), n = 1 .. 25);
Formula
G.f. for 2-compositions with all entries <= k is h(k,z)=(1-z)^2/(1-4z+2z^2+2z^{k+1}-z^{2k+2}).
G.f. for 2-compositions with largest entry k is f(k,z)=h(k,z)-h(k-1,z).
G.f. = G(z)=Sum(k*f(k,z),k=1..infinity).
Comments