Logarithmically Concave Sequence

Author

Eric W. Weisstein
August 7, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/LogarithmicallyConcaveSequence.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/LogarithmicallyConcaveSequence.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Code

LogConcaveQ[a_List]:=Module[{p=Partition[a,3,1]},
If[Length[p]==1,
p[[1,2]]^2≥p[[1,1]]p[[1,3]],
#2^2≥#1#3&@@@And@@p]
]

Examples

Table[LogConcaveQ[Flatten[Table[Binomial[n,k],{k,0,n}]]],{n,10}]

LogConcaveQ[{1,7,4,2,1}]