A172556 - OEIS

%I #19 Oct 13 2024 19:02:58

%S 1,20,1860,297200,60871300,14367744720,3718394156400,1026608414145600,

%T 297348703692826500,89365729945562642000,27658131940039664137360,

%U 8766913970029589057611200,2834492178580299130305958000,931874436031756882451601080000,310768686646948895430510472680000

%N Number of 2*n X 6 binary arrays with row sums 3 and column sums n.

%H Christoph Koutschan, <a href="/A172556/b172556.txt">Table of n, a(n) for n = 0..387</a> (terms n=1..49 from R. H. Hardin)

%H Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, <a href="https://arxiv.org/abs/2410.07435">The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices</a>, arXiv:2410.07435 [math.CO], 2024.

%F (n+3) * (n+4)^5 * (33*n^2 + 176*n + 236) * a(n+4) = 2 * (n+3) * (2*n + 7) * (3201*n^6 + 61886*n^5 + 497179*n^4 + 2124170*n^3 + 5089654*n^2 + 6484024*n + 3431096) * a(n+3) + 16 * (2*n + 5) * (2*n + 7) * (2772*n^6 + 48048*n^5 + 344379*n^4 + 1307394*n^3 + 2775099*n^2 + 3125336*n + 1460132) * a(n+2) - 128 * (n+2) * (2*n + 3) * (2*n + 5) * (2*n + 7) * (7491*n^4 + 84898*n^3 + 351364*n^2 + 628997*n + 414370) * a(n+1) + 51200 * (n+1) * (n+2) * (2*n + 1) * (2*n + 3) * (2*n + 5) * (2*n + 7) * (33*n^2  + 242*n + 445) * a(n). - _Doron Zeilberger_ and _Christoph Koutschan_, Oct 13 2024

%Y Column k=3 of A376935.

%K nonn

%O 0,2

%A _R. H. Hardin_, Feb 06 2010

%E a(0)=1 prepended by _Andrew Howroyd_, Oct 12 2024