Mathematica package --- rlog

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Abstract:This package provides a computer proof on the
r-log-convexity of P-recursive sequences.
For example, the Motzkin numbers M_n satisify

3 (1 + n) M_n + (5 + 2 n) M_{n+1} - (4 + n) M_{n+2} = 0.

So the annihilator operator is

L = 3 (1 + n) + (5 + 2 n) N - (4 + n) N^2

By the command

rLogBound[L, n, N, {1, 1, 2}, 1, 3],

we find that for n>=75, the sequence is 1-log-convex.
As a by-product, we find that for n>=75,

3+191/(16 n^2)-9/(2 n)<=M_{n+1}/M_n<=3+223/(16 n^2)-9/(2 n)

Translation or Not:no

CN No.:null