A332748 - OEIS

A332748

The number of permutations of {1,1,1,2,2,2,...,n,n,n} such that each triple of k's (k=1..n) is equally spaced with b(k) other elements in between and b(1) >= b(2) >= ... >= b(n).

1, 1, 4, 18, 124, 738, 7464, 55890, 668778, 7030210, 90713844, 1054221258, 18597735744, 242795838520

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

EXAMPLE

n = 1 case:

| | b(1)

-----+-----------+------

1 | [1, 1, 1] | [0] *

n = 2 case:

| | b(1),b(2)

-----+--------------------+----------

1 | [2, 2, 2, 1, 1, 1] | [0, 0]

2 | [2, 1, 2, 1, 2, 1] | [1, 1]

3 | [1, 2, 1, 2, 1, 2] | [1, 1]

4 | [1, 1, 1, 2, 2, 2] | [0, 0]

n = 3 case:

| | b(1),b(2),b(3)

-----+-----------------------------+---------------

1 | [3, 3, 3, 2, 2, 2, 1, 1, 1] | [0, 0, 0]

2 | [3, 3, 3, 2, 1, 2, 1, 2, 1] | [1, 1, 0]

3 | [3, 3, 3, 1, 2, 1, 2, 1, 2] | [1, 1, 0]

4 | [3, 3, 3, 1, 1, 1, 2, 2, 2] | [0, 0, 0]

5 | [3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2]

6 | [3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2]

7 | [1, 3, 3, 3, 1, 2, 2, 2, 1] | [3, 0, 0]

8 | [2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2]

9 | [1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2]

10 | [2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]

11 | [1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2]

12 | [2, 2, 2, 3, 3, 3, 1, 1, 1] | [0, 0, 0]

13 | [1, 1, 1, 3, 3, 3, 2, 2, 2] | [0, 0, 0]

14 | [1, 2, 2, 2, 1, 3, 3, 3, 1] | [3, 0, 0]

15 | [2, 2, 2, 1, 1, 1, 3, 3, 3] | [0, 0, 0]

16 | [2, 1, 2, 1, 2, 1, 3, 3, 3] | [1, 1, 0]

17 | [1, 2, 1, 2, 1, 2, 3, 3, 3] | [1, 1, 0]

18 | [1, 1, 1, 2, 2, 2, 3, 3, 3] | [0, 0, 0]

* (strongly decreasing)

CROSSREFS

Column k=3 of A332762.

Cf. A104429, A059108, A261516 (strongly decreasing), A322178, A332752.

Sequence in context: A292500 A228065 A317377 * A215691 A359460 A073511

Adjacent sequences: A332745 A332746 A332747 * A332749 A332750 A332751

KEYWORD

nonn,more

AUTHOR

Seiichi Manyama, Feb 21 2020

EXTENSIONS

a(10)-a(13) from Max Alekseyev, Sep 26 2023

STATUS

approved