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A102113 Iccanobirt numbers (3 of 15): a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)), where R is the digit reversal function A004086.

%I A102113 #14 Sep 10 2016 13:31:23
%S A102113 0,0,1,1,2,4,7,13,24,62,135,203,760,1593,1962,5980,12622,16208,39724,
%T A102113 142606,265660,914694,1587497,2150478,10594748,27283111,120773124,
%U A102113 216660897,649176190,1868619823,2758358381,6139199008,11266906261
%N A102113 Iccanobirt numbers (3 of 15): a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)), where R is the digit reversal function A004086.
%C A102113 Digit reversal variation of tribonacci numbers A000073.
%C A102113 Inspired by Iccanobif numbers: A001129, A014258-A014260.
%H A102113 Alois P. Heinz, <a href="/A102113/b102113.txt">Table of n, a(n) for n = 0..1000</a>
%F A102113 A004086(a(n)) = A102121(n).
%p A102113 R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
%p A102113 a:= proc(n) option remember; `if`(n<3, binomial(n, 2),
%p A102113        a(n-1) + R(a(n-2)) + R(a(n-3)) )
%p A102113     end:
%p A102113 seq(a(n), n=0..50);  # _Alois P. Heinz_, Jun 18 2014
%t A102113 R[n_]:=FromDigits[Reverse[IntegerDigits[n]]];Clear[a];a[0]=0;a[1]=0;a[2]=1;a [n_]:=a[n]=a[n-1]+R[a[n-2]]+R[a[n-3]];Table[a[n], {n, 0, 40}]
%t A102113 nxt[{a1_,a2_,a3_}]:={a2,a3,a3+FromDigits[Reverse[IntegerDigits[ a1]]]+ FromDigits[ Reverse[ IntegerDigits[a2]]]}; Transpose[NestList[nxt,{0,0,1},40]][[1]] (* _Harvey P. Dale_, Oct 17 2012 *)
%t A102113 nxt[{a_,b_,c_}]:={b,c,c+IntegerReverse[b]+IntegerReverse[a]}; NestList[ nxt,{0,0,1},40][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 10 2016 *)
%Y A102113 Cf. A102111-A102125.
%K A102113 nonn,base,easy
%O A102113 0,5
%A A102113 _Jonathan Vos Post_ and _Ray Chandler_, Dec 30 2004