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 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 (list; graph; refs; listen; history; text; internal format)
 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[i-1] + 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

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