A318405 Rectangular array R read by antidiagonals: R(n,k) = F(n+1)^k - k*F(n-1)*F(n)^(k-1), where F(n) = A000045(n), the n-th Fibonacci number; n >= 0, k >= 1.
0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 5, 5, 3, 1, 1, 12, 15, 13, 5, 1, 1, 27, 49, 71, 34, 8, 1, 1, 58, 163, 409, 287, 89, 13, 1, 1, 121, 537, 2315, 2596, 1237, 233, 21, 1, 1, 248, 1739, 12709, 23393, 18321, 5205, 610, 34, 1, 1, 503, 5537, 67919, 205894, 268893, 124177, 22105, 1597, 55
Offset: 0
Examples
The rectangular array R(n,k) begins: n\k| 1 2 3 4 5 6 7 ---+------------------------------------------------------------- 0 | 0 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 2 | 1 2 5 12 27 58 121 3 | 2 5 15 49 163 537 1739 4 | 3 13 71 409 2315 12709 67919 5 | 5 34 287 2596 23393 205894 1769027 6 | 8 89 1237 18321 268893 3843769 53573477 7 | 13 233 5205 124177 2941661 67944057 1530787237
Links
- A. Radhakrishnan, L. Solus, and C. Uhler. Counting Markov equivalence classes for DAG models on trees, arXiv:1706.06091 [math.CO], 2017; Discrete Applied Mathematics 244 (2018): 170-185.
Programs
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Sage
def R(n, k): return fibonacci(n+1)^k-k*fibonacci(n-1)*fibonacci(n)^(k-1)
Comments