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A253498 Number of (4+1) X (n+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally. 1

%I #8 Dec 16 2018 07:11:58

%S 3639,4720,6931,10477,18526,37469,82676,194708,483572,1255700,3383156,

%T 9387668,26645492,76907540,224670836,661915028,1961556212,5836296980,

%U 17412153716,52042992788,155742047732,466452288020,1397809159796

%N Number of (4+1) X (n+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

%H R. H. Hardin, <a href="/A253498/b253498.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>9.

%F Empirical: a(n) = 400*3^(n-3) + 738*2^(n-1) + 3044 for n>6.

%F Empirical g.f.: x*(3639 - 17114*x + 18640*x^2 - 1023*x^3 + 3585*x^4 - 26*x^5 - 1214*x^6 - 345*x^7 - 54*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Dec 16 2018

%e Some solutions for n=4:

%e ..2..2..1..1..1....0..2..2..2..2....0..2..2..2..1....0..2..2..2..2

%e ..1..1..0..0..0....1..1..1..1..1....1..1..1..1..0....2..2..2..2..2

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

%e ..2..2..1..1..1....0..0..0..0..0....1..1..1..1..0....2..2..2..2..2

%e ..2..2..1..1..2....0..0..0..0..1....2..2..2..2..1....0..0..0..0..1

%Y Row 4 of A253495.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 02 2015

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Last modified April 17 03:42 EDT 2024. Contains 371756 sequences. (Running on oeis4.)