Some Properties of Convolved 𝑘-Fibonacci Numbers

Table 1

𝐹^(𝑟)_1,𝑛, with 𝑟=1,2,3,4,5,6,7,8….

𝑛	𝐹^(1)1,𝑛	𝐹^(2)1,𝑛	𝐹^(3)1,𝑛	𝐹^(4)1,𝑛	𝐹^(5)1,𝑛	𝐹^(6)1,𝑛	𝐹^(7)1,𝑛	𝐹^(8)1,𝑛
0	0	0	0	0	0	0	0	0
1	1	1	1	1	1	1	1	1
2	1	2	3	4	5	6	7	8
3	2	5	9	14	20	27	35	44
4	3	10	22	40	65	98	140	192
5	5	20	51	105	190	315	490	726
6	8	38	111	256	511	924	1554	2472
7	13	71	233	594	1295	2534	4578	7776
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮