The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A189604 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A189604

Number of n X 3 array permutations with each element not moving, or moving one space E, S or NW.
(history; published version)

#20 by Michael De Vlieger at Tue Feb 08 22:26:16 EST 2022

STATUS

proposed

approved

#19 by Jon E. Schoenfield at Tue Feb 08 22:21:40 EST 2022

STATUS

editing

proposed

#18 by Jon E. Schoenfield at Tue Feb 08 22:21:38 EST 2022

NAME

Number of nX3 n X 3 array permutations with each element not moving, or moving one space E, S or NW.

COMMENTS

Binomial transform of A006131 starting (1, 5, 9, 29, 65, ...). - Gary W. Adamson, Feb 19 2014

FORMULA

Empirical: a(n) = 3*a(n-1) + 2*a(n-2).

G.f.: (x+3*x^2)/(1-3*x-2*x^2) [From _. - _Vladimir Kruchinin_, May 13 2011]

EXAMPLE

Some solutions for 4X34 X 3:

..4..5..1....0..5..1....0..1..2....0..1..2....4..0..1....0..1..2....4..1..2

..0..3..2....7..4..2....3..4..5....3..4..5....7..3..2....3..8..5....0..3..5

..6..7..8....3..6..8....6.11..8...10..7..8...10.11..5....6..4..7....6..7..8

..9.10.11....9.10.11....9..7.10....6..9.11....6..9..8....9.10.11....9.10.11

.

4 5 1 0 5 1 0 1 2 0 1 2

0 3 2 7 4 2 3 4 5 3 4 5

6 7 8 3 6 8 6 11 8 10 7 8

9 10 11 9 10 11 9 7 10 6 9 11

.

4 0 1 0 1 2 4 1 2

7 3 2 3 8 5 0 3 5

10 11 5 6 4 7 6 7 8

6 9 8 9 10 11 9 10 11

STATUS

approved

editing

#17 by Susanna Cuyler at Tue Sep 24 12:40:35 EDT 2019

STATUS

proposed

approved

#16 by Jean-François Alcover at Tue Sep 24 12:37:32 EDT 2019

STATUS

editing

proposed

#15 by Jean-François Alcover at Tue Sep 24 12:37:26 EDT 2019

MATHEMATICA

a[n_] := Sum[Sum[4^j Binomial[k-j+1, j], {j, 0, Quotient[k+1, 2]}]* Binomial[n-1, k], {k, 0, n-1}];

a /@ Range[1, 24] (* Jean-François Alcover, Sep 24 2019, after Gary W. Adamson *)

STATUS

approved

editing

#14 by N. J. A. Sloane at Sat Feb 22 20:32:36 EST 2014

STATUS

proposed

approved

#13 by Michel Marcus at Thu Feb 20 00:59:02 EST 2014

STATUS

editing

proposed

#12 by Michel Marcus at Thu Feb 20 00:58:47 EST 2014

NAME

Number of nX3 array permutations with each element not moving, or moving one space E, S or NW.

COMMENTS

Column 3 of A189610.

FORMULA

Empirical: a(n) = 3*a(n-1) +2*a(n-2).

CROSSREFS

Cf. A006131.

AUTHOR

R. H. Hardin , Apr 24 2011

STATUS

proposed

editing

#11 by Gary W. Adamson at Wed Feb 19 21:38:05 EST 2014

STATUS

editing

proposed