The On-Line Encyclopedia of Integer Sequences (OEIS)

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A252391

Number of (7+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 3 5 6 or 7.
(history; published version)

#8 by Alois P. Heinz at Mon Dec 03 15:35:31 EST 2018

STATUS

reviewed

approved

#7 by Michel Marcus at Mon Dec 03 12:44:09 EST 2018

STATUS

proposed

reviewed

#6 by Colin Barker at Mon Dec 03 12:19:33 EST 2018

STATUS

editing

proposed

#5 by Colin Barker at Mon Dec 03 12:19:07 EST 2018

NAME

Number of (7+2) X (n+2) 0..3 arrays with every 3X3 3 X 3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3X3 3 X 3 column and antidiagonal sum not equal to 0 3 5 6 or 7.

COMMENTS

Row 7 of A252384

FORMULA

Empirical: a(n) = 4*a(n-3) - 4*a(n-6) + a(n-9) for n>14.

Empirical g.f.: x*(1051 + 903*x + 1114*x^2 - 2843*x^3 - 1581*x^4 - 1678*x^5 + 2255*x^6 + 683*x^7 + 467*x^8 - 542*x^9 - 93*x^10 + 12*x^11 + 7*x^12 + 2*x^13) / ((1 - x)*(1 + x + x^2)*(1 - 3*x^3 + x^6)). - Colin Barker, Dec 03 2018

EXAMPLE

Some solutions for n=4:

CROSSREFS

Row 7 of A252384.

STATUS

approved

editing

#4 by R. H. Hardin at Wed Dec 17 09:00:35 EST 2014

STATUS

editing

approved

#3 by R. H. Hardin at Wed Dec 17 09:00:31 EST 2014

LINKS

R. H. Hardin, <a href="/A252391/b252391.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Wed Dec 17 09:00:16 EST 2014

NAME

allocated for R. H. Hardin

Number of (7+2)X(n+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 3 5 6 or 7

DATA

1051, 903, 1114, 1361, 2031, 2778, 3495, 5195, 7123, 9045, 13466, 18506, 23568, 35117, 48310, 61587, 91799, 126339, 161121, 240194, 330622, 421704, 628697, 865442, 1103919, 1645811, 2265619, 2889981, 4308650, 5931330, 7565952, 11280053

OFFSET

1,1

COMMENTS

Row 7 of A252384

FORMULA

Empirical: a(n) = 4*a(n-3) -4*a(n-6) +a(n-9) for n>14

EXAMPLE

Some solutions for n=4

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

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

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

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

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Dec 17 2014

STATUS

approved

editing

#1 by R. H. Hardin at Wed Dec 17 08:41:46 EST 2014

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved