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a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)) where a(0)=a(1)=a(2)=1 and R(k) = A004086(k) is the reverse of k.
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%I #9 Jun 17 2021 08:19:53

%S 1,1,1,3,5,9,17,31,111,195,319,1021,2525,4639,11092,25708,64083,

%T 173846,292644,979061,2073724,2680995,7115676,17380240,30136219,

%U 41109707,136581181,298634398,550610143,1625232666,2859685613,9863026929,19691221772,32153295043

%N a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)) where a(0)=a(1)=a(2)=1 and R(k) = A004086(k) is the reverse of k.

%p R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):

%p a:= proc(n) option remember; `if`(n<3, 1,

%p a(n-1) + R(a(n-2)) + R(a(n-3)))

%p end:

%p seq(a(n), n=0..33); # _Alois P. Heinz_, Jun 17 2021

%Y Cf. A000213, A004086.

%K easy,base,nonn

%O 0,4

%A _Felice Russo_, Sep 11 2002

%E Corrected and extended by _David Garber_, Oct 23 2002

%E Offset corrected by and more terms from _Alois P. Heinz_, Jun 17 2021