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
Examples
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
Links
- 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
Programs
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PARI
See Links section.
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.
Comments