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 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. 1
 2, 9, 38, 149, 562, 2066, 7474, 26737, 94900, 334909, 1176842, 4121632, 14397370, 50185498, 174628420, 606755258, 2105552976, 7298685677, 25275876584, 87457546835, 302382185770, 1044756677132, 3607460520006, 12449135054480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n)=Sum(A181338(n,k),k=0..n). 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. LINKS 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). EXAMPLE 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. 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); CROSSREFS Cf. A181338 Sequence in context: A010750 A026591 A007224 * A291265 A037489 A037569 Adjacent sequences:  A181336 A181337 A181338 * A181340 A181341 A181342 KEYWORD nonn AUTHOR Emeric Deutsch, Oct 15 2010 STATUS approved

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Last modified October 16 05:52 EDT 2019. Contains 328045 sequences. (Running on oeis4.)