[seqfan] A marginal observation on some tables of R. H. Hardin

[Peter Luschny]

The discussion went slightly off-topic, and the old habit
to change the name of a thread when the topic changes
seems to be a forgotten virtue.

But let me come back to Hardin's empirical recurrence.

I do not think that it is a coincidence that the coefficients
appear in Bala's A246117 although this is hard demonstrate
at the moment.

In the spirit of experimental math let me look also at
the recurrences a(n) and b(n) (case 2 and 3 in a more
general setup which makes Hardin's c(n) the case 4).

a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3),
b(n) = 9*b(n-1)-31*b(n-2)+51*b(n-3)-40*b(n-4)+12*b(n-5),
c(n) = 16*c(n-1)-106*c(n-2)+376*c(n-3)-769*c(n-4)+904*c(n-5)-564*c(n-6)+144*c(n-7).

So now my problem are meaningful initial terms,
a(0), a(1), a(2) and b(0), b(1), b(2), b(3), b(4).

Any suggestions for the initial terms?

Peter