The On-Line Encyclopedia of Integer Sequences (OEIS)

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A255094

Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 1 and no antidiagonal sum 1 and no row sum 1 and no column sum 1.
(history; published version)

#8 by Bruno Berselli at Tue Dec 18 11:11:37 EST 2018

STATUS

reviewed

approved

#7 by Michel Marcus at Tue Dec 18 10:40:16 EST 2018

STATUS

proposed

reviewed

#6 by Colin Barker at Tue Dec 18 10:38:21 EST 2018

STATUS

editing

proposed

#5 by Colin Barker at Tue Dec 18 10:38:01 EST 2018

NAME

Number of (n+2) X (1+2) 0..1 arrays with no 3x3 3 x 3 subblock diagonal sum 1 and no antidiagonal sum 1 and no row sum 1 and no column sum 1.

COMMENTS

Column 1 of A255101

FORMULA

Empirical: a(n) = 2*a(n-1) - a(n-2) + 5*a(n-3) - 2*a(n-4) + 3*a(n-5) - 2*a(n-6) - 2*a(n-7) - 2*a(n-8) - 2*a(n-9) + 2*a(n-11) for n>12.

Empirical g.f.: x*(36 + 5*x + 61*x^2 - 42*x^3 + 19*x^4 - 67*x^5 - 58*x^6 - 52*x^7 - 26*x^8 + 24*x^9 + 38*x^10 - 2*x^11) / ((1 - x)*(1 - x - 5*x^3 - 3*x^4 - 6*x^5 - 4*x^6 - 2*x^7 + 2*x^9 + 2*x^10)). - Colin Barker, Dec 18 2018

EXAMPLE

Some solutions for n=4:

CROSSREFS

Cf. A255101

Column 1 of A255101.

STATUS

approved

editing

#4 by R. H. Hardin at Sat Feb 14 11:54:12 EST 2015

STATUS

editing

approved

#3 by R. H. Hardin at Sat Feb 14 11:54:08 EST 2015

LINKS

R. H. Hardin, <a href="/A255094/b255094.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Sat Feb 14 11:53:40 EST 2015

NAME

allocated for R. H. Hardin

Number of (n+2)X(1+2) 0..1 arrays with no 3x3 subblock diagonal sum 1 and no antidiagonal sum 1 and no row sum 1 and no column sum 1

DATA

36, 77, 179, 419, 991, 2345, 5537, 13105, 31063, 73591, 174311, 412949, 978301, 2317617, 5490567, 13007447, 30815207, 73002717, 172947085, 409720065, 970646871, 2299510047, 5447651751, 12905753661, 30574362581, 72432161761

OFFSET

1,1

COMMENTS

Column 1 of A255101

FORMULA

Empirical: a(n) = 2*a(n-1) -a(n-2) +5*a(n-3) -2*a(n-4) +3*a(n-5) -2*a(n-6) -2*a(n-7) -2*a(n-8) -2*a(n-9) +2*a(n-11) for n>12

EXAMPLE

Some solutions for n=4

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

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

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

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

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

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

CROSSREFS

Cf. A255101

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Feb 14 2015

STATUS

approved

editing

#1 by R. H. Hardin at Sat Feb 14 11:51:33 EST 2015

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved