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A069916 Number of log-concave compositions (ordered partitions) of n. 3
1, 1, 2, 4, 6, 9, 14, 20, 26, 36, 47, 60, 80, 102, 127, 159, 194, 236, 291, 355, 425, 514, 611, 718, 856, 1009, 1182, 1381, 1605, 1861, 2156, 2496, 2873, 3299, 3778, 4301, 4902, 5574, 6325, 7176, 8116, 9152, 10317, 11610, 13028, 14611, 16354, 18259, 20365 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

MathWorld, Logarithmically Concave Sequence.

EXAMPLE

Out of the 8 compositions of 4, only 2+1+1 and 1+1+2 are not log-concave, so a(4)=6.

MATHEMATICA

(* This program is not suitable for computing a large number of terms *)

compos[n_] := Permutations /@ IntegerPartitions[n] // Flatten[#, 1]&;

logConcaveQ[p_] := And @@ Table[p[[i]]^2 >= p[[i-1]]*p[[i+1]], {i, 2, Length[p]-1}]; a[n_] := Count[compos[n], p_?logConcaveQ]; Table[an = a[n]; Print["a(", n, ") = ", an]; a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 29 2016 *)

PROG

(Sage) def A069916(n) : return sum(all(p[i]^2 >= p[i-1] * p[i+1] for i in range(1, len(p)-1)) for p in Compositions(n)) # Eric M. Schmidt, Sep 29 2013

CROSSREFS

Cf. A070211.

Sequence in context: A328863 A218004 A034748 * A153140 A295341 A139135

Adjacent sequences:  A069913 A069914 A069915 * A069917 A069918 A069919

KEYWORD

nonn,nice

AUTHOR

Pontus von Brömssen, Apr 24 2002

STATUS

approved

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Last modified July 5 04:14 EDT 2020. Contains 335459 sequences. (Running on oeis4.)