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A253394 Number of (n+1) X (5+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. 1

%I #7 Dec 12 2018 05:58:23

%S 304,250,316,465,666,932,1269,1693,2201,2814,3527,4360,5309,6394,7611,

%T 8980,10497,12182,14031,16064,18277,20690,23299,26124,29161,32430,

%U 35927,39672,43661,47914,52427,57220,62289,67654,73311,79280,85557,92162,99091

%N Number of (n+1) X (5+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.

%H R. H. Hardin, <a href="/A253394/b253394.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>13.

%F Empirical for n mod 2 = 0: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 164 for n>8.

%F Empirical for n mod 2 = 1: a(n) = (4/3)*n^3 + 13*n^2 + (5/3)*n + 161 for n>8.

%F Empirical g.f.: x*(304 - 662*x + 174*x^2 + 625*x^3 - 509*x^4 + 50*x^5 + 37*x^6 + 3*x^7 - 9*x^8 + 5*x^9 - 2*x^10 - x^11 + x^12) / ((1 - x)^4*(1 + x)). - _Colin Barker_, Dec 12 2018

%e Some solutions for n=4:

%e ..0..0..0..0..0..1....0..0..0..0..1..1....1..1..1..1..1..1....1..1..0..1..0..1

%e ..0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..0..0....1..1..0..1..0..1

%e ..0..0..0..0..0..0....0..0..0..0..0..1....1..1..1..1..1..1....1..1..0..1..0..1

%e ..0..0..0..0..1..0....0..0..0..0..0..1....1..1..0..0..0..0....1..1..0..1..0..1

%e ..1..1..1..0..1..0....1..1..1..1..0..1....1..1..1..1..1..1....1..1..0..1..0..1

%Y Column 5 of A253397.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 31 2014

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)