A172556 Number of 2*n X 6 binary arrays with row sums 3 and column sums n.

1, 20, 1860, 297200, 60871300, 14367744720, 3718394156400, 1026608414145600, 297348703692826500, 89365729945562642000, 27658131940039664137360, 8766913970029589057611200, 2834492178580299130305958000, 931874436031756882451601080000, 310768686646948895430510472680000

Offset

0,2

Links

Christoph Koutschan, Table of n, a(n) for n = 0..387 (terms n=1..49 from R. H. Hardin)

Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices, arXiv:2410.07435 [math.CO], 2024.

Formula

(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

Crossrefs

Column k=3 of A376935.

Sequence in context: A177297 A014606 A330196 * A246619 A222973 A267575

Adjacent sequences: A172553 A172554 A172555 * A172557 A172558 A172559

Keyword

nonn

Author

R. H. Hardin, Feb 06 2010

Extensions

a(0)=1 prepended by Andrew Howroyd, Oct 12 2024

Status

approved