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 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
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS Row index n begins with 0, column index begins with 1. 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. 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. EXAMPLE 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 PROG (Sage) def R(n, k):     return fibonacci(n+1)^k-k*fibonacci(n-1)*fibonacci(n)^(k-1) CROSSREFS Columns include A000045, A001519, A318376, A318404. Cf. A007984. Sequence in context: A178304 A123585 A145668 * A181645 A129104 A232648 Adjacent sequences:  A318402 A318403 A318404 * A318406 A318407 A318408 KEYWORD nonn,tabl,easy AUTHOR Liam Solus, Aug 26 2018 STATUS approved

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)