Batch of mystery sequences

[Gerald McGarvey]

For each of the sequences it appears that (a(n+3)+a(n+2)-a(n+1)+a(n)) / a(n+3)
approaches 0 and (a(n+2)-a(n+1)+a(n)) / a(n+3) approaches 1
as n goes to infinity

Gerald

At 10:11 PM 8/1/2005, Ross La Haye wrote:

>I suspect your number will converge to the tribonacci constant...
>
>http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?An
>um=A058265
>
>Hopefully, this helps...
>
>Ross
>
>
>
>-----Original Message-----
>From: Creighton Dement [mailto:crowdog at crowdog.de]
>Sent: Monday, August 01, 2005 5:54 PM
>To: seqfan at ext.jussieu.fr
>Subject: Batch of mystery sequences
>
>
>Dear Seqfans,
>
>It is rare (to now) that a floretion-generated integer sequence should
>follow such an obvious sign pattern with, in addition, a(n+1)/a(n)
>apparently converging to the number 1.8392868... but with no generating
>function.
>At least I can't find it with Maple. Can anyone find out how to generate
>any of the three sequences listed, below (without using FAMP)? Note: the
>paper "On the Entropy Devil's Staircase..."
>http://www.cft.edu.pl/~karol/pdf/ZB99.pdf also mentions the number
>1.8392868.  I haven't had a chance to look at it (though at first
>glance, it would appear to be way over my head, anyway...).
>
>Sincerely,
>Creighton
>
>2tessumseq: -1, 2, -6, 14, -21, 40, -70, 134, -243, 454, -833, 1535,
>-2825, 5202, -9568, 17608, -32385, 59574, -109579, 201553, -370721,
>681871, -1254156, 2306765, -4242807, 7803749, -14353340, 26399924,
>-48557036, 89310323, -164267305
>
>2jbasejsumseq: 0, -1, 3, -10, 16, -27, 45, -86, 162, -301, 554, -1019,
>1873, -3447, 6346, -11676, 21478, -39506, 72665, -133656, 245836,
>-452169, 831672, -1529684, 2813531, -5174894, 9518123, -17506565,
>32199596, -59224297, 108930470
>
>2kbaseksumseq: 0, -1, 5, -12, 18, -33, 59, -114, 208, -385, 706, -1302,
>2394, -4409, 8111, -14923, 27446, -50488, 92863, -170806, 314168,
>-577850, 1062830, -1954857, 3595545, -6613246, 12163661, -22372470,
>41149390, -75685534, 139207407