Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jun 08 2018 10:02:32
%S 48,90,178,330,571,938,1478,2248,3317,4766,6690,9198,12415,16482,
%T 21558,27820,35465,44710,55794,68978,84547,102810,124102,148784,
%U 177245,209902,247202,289622,337671,391890,452854,521172,597489,682486,776882,881434
%N Number of (n+1) X 5 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.
%C Column 4 of A204651.
%H R. H. Hardin, <a href="/A204647/b204647.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7) for n>9.
%F Conjectures from _Colin Barker_, Jun 08 2018: (Start)
%F G.f.: x*(48 - 150*x + 160*x^2 + 10*x^3 - 167*x^4 + 145*x^5 - 43*x^6 - 5*x^7 + 4*x^8) / ((1 - x)^6*(1 + x)).
%F a(n) = (1920 + 9776*n + 3480*n^2 + 540*n^3 + 90*n^4 + 4*n^5)/480 for n>2 and even.
%F a(n) = (1950 + 9776*n + 3480*n^2 + 540*n^3 + 90*n^4 + 4*n^5)/480 for n>2 and odd.
%F (End)
%e Some solutions for n=5:
%e ..0..0..0..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..0..0..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
%e ..0..0..1..1..1....0..0..0..0..0....0..0..0..1..1....0..0..0..0..0
%e ..1..1..1..1..1....0..0..0..0..1....0..0..0..1..1....0..0..0..0..1
%e ..1..1..1..1..1....0..0..0..0..1....0..1..1..1..1....0..0..0..1..1
%e ..1..1..1..1..1....0..0..0..1..0....0..1..1..1..1....0..0..1..1..1
%Y Cf. A204651.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 17 2012