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.

0, 0, 1, 1, 2, 4, 7, 13, 24, 62, 135, 203, 760, 1593, 1962, 5980, 12622, 16208, 39724, 142606, 265660, 914694, 1587497, 2150478, 10594748, 27283111, 120773124, 216660897, 649176190, 1868619823, 2758358381, 6139199008, 11266906261

Offset: 0

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Keywords

• nonn
• base
• easy

Comments

Digit reversal variation of tribonacci numbers A000073.

Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A102111-A102125.

Programs

Maple

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
a:= proc(n) option remember; `if`(n<3, binomial(n, 2),
       a(n-1) + R(a(n-2)) + R(a(n-3)) )
    end:
seq(a(n), n=0..50);  # Alois P. Heinz, Jun 18 2014

Mathematica

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}]
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 *)
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 *)

Formula

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