A102111 Iccanobirt numbers (1 of 15): a(n) = a(n-1) + a(n-2) + R(a(n-3)), where R is the digit reversal function A004086.

0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 99, 185, 328, 612, 1521, 2956, 4693, 8900, 20185, 33049, 53332, 144483, 291848, 459666, 1135955, 2443813, 4246722, 12285846, 19716010, 34278280, 118852511, 154192582, 281332336, 550783729, 1117407516, 2301424427

Offset

0,5

Comments

Digit reversal variation of tribonacci numbers A000073.

Inspired by Iccanobif numbers: A001129, A014258-A014260.

Links

Table of n, a(n) for n=0..35.

Formula

A004086(a(n)) = A102119(n).

Maple

read("transforms") ;
A102111 := proc(n)
    option remember;
    if n <= 2 then
        return op(n+1, [0, 0, 1]) ;
    else
        return procname(n-1)+procname(n-2)+digrev(procname(n-3)) ;
    end if;
end proc:
seq(A102111(n), n=0..20) ; # R. J. Mathar, Nov 17 2012

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]+a[n-2]+R[a[n-3]]; Table[a[n], {n, 0, 40}]
nxt[{a_, b_, c_}]:={b, c, IntegerReverse[a]+b+c}; NestList[nxt, {0, 0, 1}, 40][[;; , 1]] (* Harvey P. Dale, Jul 18 2023 *)

Prog

(Python)
def R(n):
  n_str = str(n)
  reversedn_str = n_str[::-1]
  reversedn = int(reversedn_str)
  return reversedn
def A(n):
  if n == 0:
    return 0
  elif n == 1:
    return 0
  elif n == 2:
    return 1
  elif n >= 3:
    return A(n-1)+A(n-2)+R(A(n-3))
for i in range(0, 20):
  print(A(i)) # Dylan Delgado, Oct 23 2019
(Magma) a:=[0, 0, 1]; [n le 3 select a[n] else Self(n-1) + Self(n-2) + Seqint(Reverse(Intseq(Self(n-3)))):n in [1..36]]; // Marius A. Burtea, Oct 23 2019

Crossrefs

Cf. A102112-A102125, A102131, A102171.

Sequence in context: A160254 A276661 A005318 * A224704 A265826 A059633

Adjacent sequences: A102108 A102109 A102110 * A102112 A102113 A102114

Keyword

nonn,base,easy

Author

Jonathan Vos Post and Ray Chandler, Dec 30 2004

Status

approved