

A070211


Number of compositions (ordered partitions) of n that are concave sequences.


2



1, 1, 2, 4, 6, 9, 14, 18, 24, 34, 42, 52, 68, 82, 101, 126, 147, 175, 213, 246, 289, 344, 392, 453, 530, 598, 687, 791, 885, 1007, 1151, 1276, 1438, 1629, 1806, 2018, 2262, 2490, 2775, 3091, 3387, 3754, 4165, 4542, 5011, 5527, 6012, 6600, 7245, 7864, 8614
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OFFSET

0,3


COMMENTS

Here, a finite sequence is concave if each term (other than the first or last) is at least the average of the two adjacent terms.  Eric M. Schmidt, Sep 29 2013


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500


EXAMPLE

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


PROG

(Sage) def A070211(n) : return sum(all(2*p[i] >= p[i1] + p[i+1] for i in xrange(1, len(p)1)) for p in Compositions(n)) # Eric M. Schmidt, Sep 29 2013


CROSSREFS

Cf. A069916.
Cf. A001523 (weakly unimodal compositions).
Sequence in context: A253108 A198201 A281989 * A113753 A024457 A117842
Adjacent sequences: A070208 A070209 A070210 * A070212 A070213 A070214


KEYWORD

nice,nonn


AUTHOR

Pontus von BrÃ¶mssen, May 07 2002


STATUS

approved



