A201501 - OEIS

%I #9 May 23 2018 08:11:37

%S 2,3,12,12,40,32,98,73,204,141,380,252,650,414,1042,649,1590,967,2330,

%T 1394,3302,1944,4550,2649,6122,3523,8070,4604,10450,5910,13320,7483,

%U 16744,9343,20790,11538,25528,14090,31032,17053,37382,20451,44660,24342

%N Number of n X 5 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%C Column 5 of A201503.

%H R. H. Hardin, <a href="/A201501/b201501.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-3) +a(n-4) +2*a(n-5) -4*a(n-6) +2*a(n-7) +2*a(n-8) -4*a(n-9) +4*a(n-11) -2*a(n-12) -2*a(n-13) +4*a(n-14) -2*a(n-15) -a(n-16) +3*a(n-17) -2*a(n-18) -a(n-19) +a(n-20).

%F Even terms are A188183((n-2)/2).

%F Empirical g.f.: x*(2 + x + 5*x^2 + 11*x^4 - 3*x^5 + 12*x^6 + 3*x^7 + 5*x^8 - x^9 + 12*x^10 - 3*x^11 - x^12 + 5*x^13 - 2*x^14 - x^15 + 3*x^16 - 2*x^17 - x^18 + x^19) / ((1 - x)^5*(1 + x)^5*(1 - x + x^2)*(1 + x^2)^2*(1 + x^4)). - _Colin Barker_, May 23 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A201503.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 02 2011