cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A318405 #20 Mar 16 2020 13:06:02
%S A318405 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 A318405 58,163,409,287,89,13,1,1,121,537,2315,2596,1237,233,21,1,1,248,1739,
%U A318405 12709,23393,18321,5205,610,34,1,1,503,5537,67919,205894,268893,124177,22105,1597,55
%N 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.
%C A318405 Row index n begins with 0, column index begins with 1.
%C A318405 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 A318405 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 A318405 The rectangular array R(n,k) begins:
%e A318405 n\k|   1      2      3        4         5          6            7
%e A318405 ---+-------------------------------------------------------------
%e A318405 0  |   0      1      1        1         1          1            1
%e A318405 1  |   1      1      1        1         1          1            1
%e A318405 2  |   1      2      5       12        27         58          121
%e A318405 3  |   2      5     15       49       163        537         1739
%e A318405 4  |   3     13     71      409      2315      12709        67919
%e A318405 5  |   5     34    287     2596     23393     205894      1769027
%e A318405 6  |   8     89   1237    18321    268893    3843769     53573477
%e A318405 7  |  13    233   5205   124177   2941661   67944057   1530787237
%o A318405 (Sage)
%o A318405 def R(n, k):
%o A318405     return fibonacci(n+1)^k-k*fibonacci(n-1)*fibonacci(n)^(k-1)
%Y A318405 Columns include A000045, A001519, A318376, A318404.
%Y A318405 Cf. A007984.
%K A318405 nonn,tabl,easy
%O A318405 0,9
%A A318405 _Liam Solus_, Aug 26 2018