A101330 -id:A101330 - cp's OEIS frontend

A101361 a(1) = a(2) = 1; for n > 2, a(n) = Knuth's Fibonacci (or circle) product "a(n-1) o a(n-2)".

1, 1, 3, 8, 55, 987, 121393, 267914296, 72723460248141, 43566776258854844738105, 7084593923980518516849609894969925639, 690168906931029935139391829792095612517948949963798093315456

Offset: 1

N. J. A. Sloane, Jan 26 2005

			1o1 = 3, 1o3 = 8, 3o8 = 55, ...

Alois P. Heinz, Table of n, a(n) for n = 1..17
D. E. Knuth, Fibonacci multiplication, Appl. Math. Lett. 1 (1988), 57-60.

Cf. A000045, A101330.

with(combinat); f:=n->fibonacci(2*fibonacci(n));
# second Maple program:
F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
a:= n-> F(2*F(n)):
seq(a(n), n=1..12);  # Alois P. Heinz, Jan 20 2017

Table[ Fibonacci[2Fibonacci[n]], {n, 12}] (* Robert G. Wilson v, Feb 12 2005 *)

a(n)=if(n<1,0,fibonacci(2*fibonacci(n)))

a(n) = Fibonacci(2*Fibonacci(n)).

Third-order nonlinear recursion: a(0)=1, a(1)=1, a(2)=3, a(n)=(a(n-1)^2 - a(n-2)^2)/a(n-3). - T. D. Noe, Mar 17 2009

Formula and more terms from Michael Somos, Feb 03 2005

A356592 Array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) = Sum_{i, j >= 3} t_i * u_j * T(i+j) where Sum_{i >= 3} t_i * T(i) and Sum_{j >= 3} u_j * T(j) are the greedy tribonacci representations of n and k, respectively, and T = A000073.

Original entry on oeis.org

0, 0, 0, 0, 7, 0, 0, 13, 13, 0, 0, 20, 24, 20, 0, 0, 24, 37, 37, 24, 0, 0, 31, 44, 57, 44, 31, 0, 0, 37, 57, 68, 68, 57, 37, 0, 0, 44, 68, 88, 81, 88, 68, 44, 0, 0, 51, 81, 105, 105, 105, 105, 81, 51, 0, 0, 57, 94, 125, 125, 136, 125, 125, 94, 57, 0

Offset: 0

Rémy Sigrist, Sep 11 2022

This sequence is to tribonacci numbers (A000073) what A135090 is to Fibonacci numbers (A000045).

			Array A(n, k) begins:
  n\k | 0   1    2    3    4    5    6    7    8    9   10
  ----+---------------------------------------------------
    0 | 0   0    0    0    0    0    0    0    0    0    0
    1 | 0   7   13   20   24   31   37   44   51   57   64
    2 | 0  13   24   37   44   57   68   81   94  105  118
    3 | 0  20   37   57   68   88  105  125  145  162  182
    4 | 0  24   44   68   81  105  125  149  173  193  217
    5 | 0  31   57   88  105  136  162  193  224  250  281
    6 | 0  37   68  105  125  162  193  230  267  298  335
    7 | 0  44   81  125  149  193  230  274  318  355  399
    8 | 0  51   94  145  173  224  267  318  369  412  463
    9 | 0  57  105  162  193  250  298  355  412  460  517
   10 | 0  64  118  182  217  281  335  399  463  517  581

A. Messaoudi, Tribonacci multiplication, Appl. Math. Lett. 15 (2002), 981-985.
Rémy Sigrist, PARI program
Index entries for sequences related to Zeckendorf expansion of n

Cf. A000045, A000073, A101330, A135090.

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A(n, 0) = A(0, k) = 0.
A(n, k) = A(k, n).
A(m, A(n, k)) = A(A(m, n), k) for m, n, k >= 5.

cp's OEIS Frontend

A101361 a(1) = a(2) = 1; for n > 2, a(n) = Knuth's Fibonacci (or circle) product "a(n-1) o a(n-2)".

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