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Number of nX4 binary arrays whose sum with another nX4 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order
1

%I #4 May 22 2013 10:37:21

%S 15,138,1178,9113,61808,361361,1825607,8065278,31631401,111785599,

%T 360788468,1075829429,2993017696,7832960008,19417916324,45865067963,

%U 103734768130,225619306783,473616394498,962612525277,1899542726132

%N Number of nX4 binary arrays whose sum with another nX4 binary array containing no more than two 1s has rows and columns in lexicographically nondecreasing order

%C Column 4 of A225982

%H R. H. Hardin, <a href="/A225978/b225978.txt">Table of n, a(n) for n = 1..76</a>

%F Empirical: a(n) = (23/14820309504000)*n^17 + (397/2615348736000)*n^16 + (1429/217945728000)*n^15 + (21083/130767436800)*n^14 + (156407/62270208000)*n^13 + (375707/14370048000)*n^12 + (3136061/16765056000)*n^11 + (21563/22861440)*n^10 + (26402329/6096384000)*n^9 + (423919927/18289152000)*n^8 + (68634593/598752000)*n^7 + (144700261/1437004800)*n^6 + (19312991563/12108096000)*n^5 - (22496273857/4540536000)*n^4 + (97668459683/3027024000)*n^3 - (41460631/700700)*n^2 + (20134601/291720)*n - 23 for n>2

%e Some solutions for n=3

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ May 22 2013