The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A277653

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Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.
(history; published version)

#9 by Alois P. Heinz at Tue Feb 05 14:21:26 EST 2019

STATUS

reviewed

approved

#8 by Michel Marcus at Tue Feb 05 12:53:04 EST 2019

STATUS

proposed

reviewed

#7 by Colin Barker at Tue Feb 05 12:31:49 EST 2019

STATUS

editing

proposed

#6 by Colin Barker at Tue Feb 05 12:31:18 EST 2019

NAME

Number of nX2 n X 2 0..2 arrays with every element equal to some element at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

COMMENTS

Column 2 of A277659.

FORMULA

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

Empirical g.f.: x^3*(1 - x) / (1 - 3*x - 2*x^2 + 2*x^4). - Colin Barker, Feb 05 2019

EXAMPLE

All solutions for n=4:

CROSSREFS

Cf. Column 2 of A277659.

STATUS

approved

editing

#5 by R. H. Hardin at Wed Oct 26 07:39:58 EDT 2016

STATUS

editing

approved

#4 by R. H. Hardin at Wed Oct 26 07:39:54 EDT 2016

LINKS

R. H. Hardin, <a href="/A277653/b277653.txt">Table of n, a(n) for n = 1..210</a>

#3 by R. H. Hardin at Wed Oct 26 07:39:18 EDT 2016

NAME

allocated for R. H. Hardin

Number of nX2 0..2 arrays with every element equal to some element at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

DATA

0, 0, 1, 2, 8, 28, 98, 346, 1218, 4290, 15110, 53218, 187438, 660170, 2325166, 8189402, 28843662, 101589450, 357805342, 1260216122, 4438571726, 15632968522, 55060438334, 193926819802, 683024192622, 2405660280426, 8472908349854

OFFSET

1,4

COMMENTS

Column 2 of A277659.

FORMULA

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

EXAMPLE

All solutions for n=4

..0..1. .0..1

..2..2. .2..2

..1..0. .1..0

..1..2. .2..1

CROSSREFS

Cf. A277659.

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Oct 26 2016

STATUS

approved

editing

#2 by R. H. Hardin at Wed Oct 26 07:35:42 EDT 2016

KEYWORD

allocating

allocated

#1 by R. H. Hardin at Wed Oct 26 07:35:42 EDT 2016

NAME

allocated for R. H. Hardin

KEYWORD

allocating

STATUS

approved