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A266473 Number of 6Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.

%I A266473 #4 Dec 29 2015 19:59:11
%S A266473 7,29,147,794,4074,18808,77320,285494,959672,2975483,8605341,23428725,
%T A266473 60497931,149066593,352233950,801471439,1762213254,3755124007,
%U A266473 7774777259,15675004492,30833594755,59276323572,111542905766,205731574732
%N A266473 Number of 6Xn binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
%C A266473 Row 6 of A266470.
%H A266473 R. H. Hardin, <a href="/A266473/b266473.txt">Table of n, a(n) for n = 1..210</a>
%F A266473 Empirical: a(n) = (1/121645100408832000)*n^19 + (1/914624815104000)*n^18 + (37/533531142144000)*n^17 + (89/31384184832000)*n^16 + (1039/12553673932800)*n^15 + (116807/62768369664000)*n^14 + (3153461/94152554496000)*n^13 + (511019/1034643456000)*n^12 + (57504877/9656672256000)*n^11 + (48689987/877879296000)*n^10 + (475429693/1207084032000)*n^9 + (2471183497/1207084032000)*n^8 + (117295069721/23538138624000)*n^7 + (79279038437/3362591232000)*n^6 + (2282457077/12108096000)*n^5 - (6773798653/40864824000)*n^4 + (20107095509/9648639000)*n^3 - (10497092849/7718911200)*n^2 + (607842269/116396280)*n + 1
%e A266473 Some solutions for n=4
%e A266473 ..0..0..1..1....0..0..0..1....0..0..0..1....0..0..1..1....0..0..0..1
%e A266473 ..0..1..0..0....1..1..1..0....0..0..1..0....0..1..1..1....0..0..1..0
%e A266473 ..0..1..0..1....1..1..1..0....0..0..1..0....1..0..1..1....0..1..1..0
%e A266473 ..1..0..0..1....1..1..1..1....0..1..0..0....1..1..0..0....1..0..0..0
%e A266473 ..1..0..1..0....1..1..1..1....1..0..0..1....1..1..0..0....1..0..0..0
%e A266473 ..1..1..1..0....1..1..1..1....1..1..0..0....1..1..1..1....1..1..0..1
%Y A266473 Cf. A266470.
%K A266473 nonn
%O A266473 1,1
%A A266473 _R. H. Hardin_, Dec 29 2015