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Revision History for A209368

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A209368

Number of n X 2 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z.
(history; published version)

#9 by Alois P. Heinz at Mon Jul 09 14:56:45 EDT 2018

STATUS

reviewed

approved

#8 by Michel Marcus at Mon Jul 09 14:05:43 EDT 2018

STATUS

proposed

reviewed

#7 by Colin Barker at Mon Jul 09 13:34:48 EDT 2018

STATUS

editing

proposed

#6 by Colin Barker at Mon Jul 09 13:34:12 EDT 2018

NAME

Number of nX2 n X 2 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z.

COMMENTS

Column 2 of A209374.

FORMULA

Empirical: a(n) = a(n-1) + a(n-2) + 3*a(n-3) + a(n-4) - a(n-5) - a(n-6) for n>11.

Empirical g.f.: x*(8 + 31*x + 37*x^2 - 18*x^3 - 160*x^4 - 252*x^5 - 218*x^6 - 32*x^7 + 93*x^8 + 73*x^9 + 16*x^10) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Jul 09 2018

EXAMPLE

Some solutions for n=5:

CROSSREFS

Cf. A209374.

AUTHOR

R. H. Hardin , Mar 07 2012

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:37:28 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Mar 07 2012

Discussion

Sat Mar 31

12:37

OEIS Server: https://oeis.org/edit/global/875

#4 by Ron Hardin at Wed Mar 07 04:58:35 EST 2012

STATUS

editing

approved

#3 by Ron Hardin at Wed Mar 07 04:58:32 EST 2012

LINKS

R. H. Hardin, <a href="/A209368/b209368.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Wed Mar 07 04:58:14 EST 2012

NAME

allocated for Ron HardinNumber of nX2 1..3 arrays with no element with value z exactly a city block distance of z from another element with value z

DATA

8, 39, 84, 129, 178, 338, 722, 1568, 3362, 7200, 15488, 33282, 71442, 153458, 329672, 708050, 1520768, 3266568, 7016258, 15070050, 32369058, 69525632, 149333762, 320753792, 688947200, 1479788802, 3178436450, 6826961250, 14663623752

OFFSET

1,1

COMMENTS

Column 2 of A209374

FORMULA

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>11

EXAMPLE

Some solutions for n=5

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Mar 07 2012

STATUS

approved

editing

#1 by Ron Hardin at Wed Mar 07 04:54:36 EST 2012

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved