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

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.

Crossrefs

Cf. A102112-A102125, A102131, A102171.

Programs

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

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 *)

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

Formula

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