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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)