A102113 - OEIS

%I #14 Sep 10 2016 13:31:23

%S 0,0,1,1,2,4,7,13,24,62,135,203,760,1593,1962,5980,12622,16208,39724,

%T 142606,265660,914694,1587497,2150478,10594748,27283111,120773124,

%U 216660897,649176190,1868619823,2758358381,6139199008,11266906261

%N 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 Digit reversal variation of tribonacci numbers A000073.

%C Inspired by Iccanobif numbers: A001129, A014258-A014260.

%H Alois P. Heinz, <a href="/A102113/b102113.txt">Table of n, a(n) for n = 0..1000</a>

%F A004086(a(n)) = A102121(n).

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

%p a:= proc(n) option remember; `if`(n<3, binomial(n, 2),

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

%p     end:

%p seq(a(n), n=0..50);  # _Alois P. Heinz_, Jun 18 2014

%t 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 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 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 Cf. A102111-A102125.

%K nonn,base,easy

%O 0,5

%A _Jonathan Vos Post_ and _Ray Chandler_, Dec 30 2004