OFFSET
0,2
COMMENTS
1st column is the Fibonacci sequence.
REFERENCES
M. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456-4461 doi:10.1016/j.amc.2009.12.069, Table 1.
LINKS
G. C. Greubel, Table of n, a(n) for the first 100 antidiagonals, flattened
Katharine A. Ahrens, Combinatorial Applications of the k-Fibonacci Numbers: A Cryptographically Motivated Analysis, Ph. D. thesis, North Carolina State University (2020).
M. Tetiva, Subsets that make no difference d, Mathematics Magazine 84 (2011), no. 4, 300-301.
FORMULA
T(n,m) = Product_{i=0 to m} F(floor[(n + i)/(m + 1) + 2]) where F(n) is the n-th Fibonacci number.
EXAMPLE
Table begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...
5, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, ...
8, 9, 12, 16, 16, 16, 16, 16, 16, 16, 16, ...
13, 15, 18, 24, 32, 32, 32, 32, 32, 32, 32, ...
21, 25, 27, 36, 48, 64, 64, 64, 64, 64, 64, ...
34, 40, 45, 54, 72, 96, 128, 128, 128, 128, 128, ...
55, 64, 75, 81, 108, 144, 192, 256, 256, 256, 256, ...
89, 104, 125, 135, 162, 216, 288, 384, 512, 512, 512, ...
144, 169, 200, 225, 243, 324, 432, 576, 768, 1024, 1024, ...
............................................................
MATHEMATICA
a[n_, m_] := Product[Fibonacci[Floor[(n + i)/(m + 1) + 2]], {i, 0, m}]; Flatten[Table[a[j - i, i], {j, 0, 30}, {i, 0, j}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Nacin, Mar 09 2012
STATUS
approved