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A253449 Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically. 2

%I

%S 81,414,1388,3639,8501,19701,48293,126357,346997,982677,2837237,

%T 8295957,24462197,72541077,215938037,644449557,1926625397,5766435477,

%U 17272430837,51763547157,155183156597,465334505877,1395573595637,4185860948757

%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.

%C Column 1 of A253456.

%H R. H. Hardin, <a href="/A253449/b253449.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>10.

%F Empirical: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7.

%F Empirical g.f.: x*(81 - 72*x - 205*x^2 - 621*x^3 - 549*x^4 + 396*x^5 + 1764*x^6 + 2304*x^7 + 1872*x^8 + 864*x^9) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - _Colin Barker_, Mar 20 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A253456.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2015

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Last modified September 23 17:19 EDT 2021. Contains 347618 sequences. (Running on oeis4.)