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.

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

0,5

Comments

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

Links

Table of n, a(n) for n=0..65.

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

Formula

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.

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A000045, A000073, A101330, A135090.

Sequence in context: A344785 A240984 A235363 * A211904 A094898 A341806

Adjacent sequences: A356589 A356590 A356591 * A356593 A356594 A356595

Keyword

nonn,tabl

Author

Rémy Sigrist, Sep 11 2022

Status

approved