accident?

[Emeric Deutsch]

Dear fans,
I am puzzled by the extremely frequent occurrence of the 
following phenomenon.
I am looking in OEIS for the sequence 
	1, 1, 2, 5, 13, 33, 80, 185, 411, 885, 1862,...
I type in only:		1,2,5,13,33,80
The only answer is 
	1,1,1,2,5,13,33,80,184,402,840
This sequence has 	184 instead of 185,
			402 instead of 411,
			840 instead of 885.
Pretty close. It happens very often.
It seems that the first six terms determine roughly the rate 
of increase. Any more precise explanation? Thanks.
Emeric