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Revision History for A211463 (Underlined text is an addition; strikethrough text is a deletion.)

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A211463 Number of -2..2 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having three or four distinct values for every i<=n and j<=n.
(history; published version)
#8 by Alois P. Heinz at Tue Jul 17 15:44:51 EDT 2018
STATUS

reviewed

approved

#7 by Michel Marcus at Tue Jul 17 14:25:28 EDT 2018
STATUS

proposed

reviewed

#6 by Colin Barker at Tue Jul 17 13:50:01 EDT 2018
STATUS

editing

proposed

#5 by Colin Barker at Tue Jul 17 13:49:48 EDT 2018
NAME

Number of -2..2 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having three or four distinct values for every i<=n and j<=n.

FORMULA

Empirical: a(n) = 5*a(n-1) +) + 9*a(n-2) -) - 57*a(n-3) -) - 36*a(n-4) +) + 196*a(n-5) +) + 96*a(n-6) -) - 124*a(n-7) +) + 24*a(n-8)).

Empirical g.f.: 4*x*(5 - 5*x - 69*x^2 + 11*x^3 + 264*x^4 + 92*x^5 - 150*x^6 + 30*x^7) / ((1 - 2*x - 6*x^2)*(1 - x - 6*x^2 + 2*x^3)*(1 - 2*x - 5*x^2 + 2*x^3)). - Colin Barker, Jul 17 2018

EXAMPLE

Some solutions for n=5:

AUTHOR

_R. H. Hardin_ _, Apr 12 2012

STATUS

approved

editing

#4 by R. H. Hardin at Thu Apr 12 06:14:08 EDT 2012
STATUS

editing

approved

#3 by R. H. Hardin at Thu Apr 12 06:14:04 EDT 2012
LINKS

R. H. Hardin, <a href="/A211463/b211463.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Thu Apr 12 06:13:45 EDT 2012
NAME

allocated for R. H. Hardin

Number of -2..2 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having three or four distinct values for every i<=n and j<=n

DATA

20, 80, 304, 1144, 4232, 15536, 56616, 205400, 742608, 2678752, 9648024, 34716712, 124861664, 449008336, 1614830152, 5809328408, 20907961552, 75287770240, 271263934328, 977981837448, 3528166785472, 12736459731632, 46007299834152

OFFSET

1,1

FORMULA

Empirical: a(n) = 5*a(n-1) +9*a(n-2) -57*a(n-3) -36*a(n-4) +196*a(n-5) +96*a(n-6) -124*a(n-7) +24*a(n-8)

EXAMPLE

Some solutions for n=5

.-1...-2....1....2...-2....2...-1...-2....1....1...-2...-2...-1....2....1...-2

..2....1...-1....0....1...-2....1....2...-2...-2....1....2....2....0....0....0

..0....0...-2...-1....2....1...-1....1....0...-1....2....1....1...-1....1...-1

..2....1....1....2....0...-2....1...-1....2...-2...-2...-1....0....0...-2....0

.-1...-2...-1....0....1....2....0....2...-2....0....1....0...-1....1....0....2

..0....2....0....1....0....0....1...-2....0...-1....0....1....0....2....2...-1

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin Apr 12 2012

STATUS

approved

editing

#1 by R. H. Hardin at Thu Apr 12 06:09:00 EDT 2012
NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved

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Last modified August 31 15:16 EDT 2024. Contains 375572 sequences. (Running on oeis4.)