Batch of mystery sequences

[Creighton Dement]

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