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%I #20 Mar 16 2020 13:06:02
%S 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,
%T 58,163,409,287,89,13,1,1,121,537,2315,2596,1237,233,21,1,1,248,1739,
%U 12709,23393,18321,5205,610,34,1,1,503,5537,67919,205894,268893,124177,22105,1597,55
%N 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.
%C Row index n begins with 0, column index begins with 1.
%C R(n,k) is the number of Markov equivalence classes whose skeleton is a spider graph with k legs, each of which contains n nodes of degree at most two. See Corollary 4.2 in the paper by A. Radhakrishnan et al. below.
%H A. Radhakrishnan, L. Solus, and C. Uhler. <a href="https://arxiv.org/abs/1706.06091">Counting Markov equivalence classes for DAG models on trees</a>, arXiv:1706.06091 [math.CO], 2017; Discrete Applied Mathematics 244 (2018): 170-185.
%e The rectangular array R(n,k) begins:
%e n\k| 1 2 3 4 5 6 7
%e ---+-------------------------------------------------------------
%e 0 | 0 1 1 1 1 1 1
%e 1 | 1 1 1 1 1 1 1
%e 2 | 1 2 5 12 27 58 121
%e 3 | 2 5 15 49 163 537 1739
%e 4 | 3 13 71 409 2315 12709 67919
%e 5 | 5 34 287 2596 23393 205894 1769027
%e 6 | 8 89 1237 18321 268893 3843769 53573477
%e 7 | 13 233 5205 124177 2941661 67944057 1530787237
%o (Sage)
%o def R(n, k):
%o return fibonacci(n+1)^k-k*fibonacci(n-1)*fibonacci(n)^(k-1)
%Y Columns include A000045, A001519, A318376, A318404.
%Y Cf. A007984.
%K nonn,tabl,easy
%O 0,9
%A _Liam Solus_, Aug 26 2018
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