login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..65.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 04:38 EDT 2019. Contains 324318 sequences. (Running on oeis4.)