The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A253395

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Number of (n+1) X (6+1) 0..1 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.
(history; published version)

#7 by Alois P. Heinz at Wed Dec 12 06:51:47 EST 2018

STATUS

proposed

approved

#6 by Colin Barker at Wed Dec 12 05:58:47 EST 2018

STATUS

editing

proposed

#5 by Colin Barker at Wed Dec 12 05:58:23 EST 2018

NAME

Number of (n+1) X (6+1) 0..1 arrays with every 2X2 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

COMMENTS

Column 6 of A253397

FORMULA

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6) for n>16.

Empirical for n mod 2 = 0: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 357 for n>10.

Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 364 for n>10.

Empirical g.f.: x*(476 - 1584*x + 1519*x^2 + 556*x^3 - 1881*x^4 + 1054*x^5 - 48*x^6 - 106*x^7 + 20*x^8 + 12*x^9 - 23*x^10 + 17*x^11 - 5*x^12 + 2*x^14 - x^15) / ((1 - x)^5*(1 + x)). - Colin Barker, Dec 12 2018

EXAMPLE

Some solutions for n=4:

CROSSREFS

Column 6 of A253397.

STATUS

approved

editing

#4 by R. H. Hardin at Wed Dec 31 07:27:00 EST 2014

STATUS

editing

approved

#3 by R. H. Hardin at Wed Dec 31 07:26:55 EST 2014

LINKS

R. H. Hardin, <a href="/A253395/b253395.txt">Table of n, a(n) for n = 1..210</a>

#2 by R. H. Hardin at Wed Dec 31 07:26:38 EST 2014

NAME

allocated for R. H. Hardin

Number of (n+1)X(6+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically

DATA

476, 320, 419, 632, 932, 1318, 1855, 2528, 3408, 4498, 5864, 7521, 9542, 11949, 14824, 18197, 22158, 26745, 32056, 38137, 45094, 52981, 61912, 71949, 83214, 95777, 109768, 125265, 142406, 161277, 182024, 204741, 229582, 256649, 286104, 318057

OFFSET

1,1

COMMENTS

Column 6 of A253397

FORMULA

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6) for n>16

Empirical for n mod 2 = 0: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 357 for n>10

Empirical for n mod 2 = 1: a(n) = (1/6)*n^4 + (185/6)*n^2 - 61*n + 364 for n>10

EXAMPLE

Some solutions for n=4

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

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

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

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

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

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin, Dec 31 2014

STATUS

approved

editing

#1 by R. H. Hardin at Wed Dec 31 07:16:57 EST 2014

NAME

allocated for R. H. Hardin

KEYWORD

allocated

STATUS

approved