The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A264158

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A264158

Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,1 0,-1 0,2 1,0 -1,0 or 2,0.
(history; published version)

#11 by Bruno Berselli at Wed Mar 21 06:42:32 EDT 2018

STATUS

reviewed

approved

#10 by Joerg Arndt at Wed Mar 21 06:34:30 EDT 2018

STATUS

proposed

reviewed

#9 by Colin Barker at Wed Mar 21 06:31:40 EDT 2018

STATUS

editing

proposed

#8 by Colin Barker at Wed Mar 21 06:31:16 EDT 2018

NAME

Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,1 0,-1 0,2 1,0 -1,0 or 2,0.

FORMULA

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + 2*a(n-3) + 4*a(n-5) - a(n-8).

Empirical g.f.: x*(4 + 2*x + x^2 + 3*x^3 + 4*x^4 - x^6 - x^7) / (1 - 2*x - 2*x^2 - 2*x^3 - 4*x^5 + x^8). - Colin Barker, Mar 21 2018

EXAMPLE

Some solutions for n=4:

STATUS

approved

editing

#7 by R. H. Hardin at Tue Nov 10 12:03:29 EST 2015

STATUS

editing

approved

#6 by R. H. Hardin at Tue Nov 10 12:03:25 EST 2015

NAME

Number of (n+1)X(1+1) arrays of permutations of 0..n*1-2+1 with each element having directed index change 0,1 0,-1 0,2 1,0 -1,0 or 2,0.

STATUS

approved

editing

#5 by R. H. Hardin at Fri Nov 06 10:14:22 EST 2015

STATUS

editing

approved

#4 by R. H. Hardin at Fri Nov 06 10:14:18 EST 2015

LINKS

R. H. Hardin, <a href="/A264158/b264158.txt">Table of n, a(n) for n = 1..210</a>

#3 by R. H. Hardin at Fri Nov 06 10:13:47 EST 2015

NAME

allocated for R. H. Hardin

Number of (n+1)X(1+1) arrays of permutations of 0..n*1-1 with each element having directed index change 0,1 0,-1 0,2 1,0 -1,0 or 2,0.

DATA

4, 10, 29, 89, 260, 772, 2281, 6741, 19940, 58954, 174329, 515481, 1524232, 4507072, 13327105, 39407393, 116525124, 344557218, 1018833429, 3012624481, 8908135596, 26340780436, 77887982793, 230309723973, 681010947204, 2013705293106

OFFSET

1,1

COMMENTS

Column 1 of A264163.

FORMULA

Empirical: a(n) = 2*a(n-1) +2*a(n-2) +2*a(n-3) +4*a(n-5) -a(n-8)

EXAMPLE

Some solutions for n=4

..1..0....1..0....1..3....2..3....2..3....1..0....2..0....2..0....1..0....1..3

..4..5....3..2....0..2....0..1....0..1....3..2....3..5....4..1....4..5....0..5

..2..3....5..7....5..7....5..7....6..7....5..4....6..1....6..3....2..3....6..7

..7..9....4..6....4..9....4..9....4..5....8..9....8..9....8..5....8..9....2..9

..6..8....9..8....6..8....6..8....9..8....6..7....4..7....9..7....6..7....4..8

CROSSREFS

Cf. A264163.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Nov 06 2015

STATUS

approved

editing

#2 by R. H. Hardin at Fri Nov 06 10:11:55 EST 2015

KEYWORD

allocating

allocated