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A201374 Number of nX7 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.

%I A201374 #7 Jul 22 2025 16:12:13
%S A201374 2,8,44,280,2016,15574,115168,728078,3793342,16517460,61759798,
%T A201374 203474642,603403128,1638153030,4126393250,9747403504,21778931370,
%U A201374 46349684784,94496712184,185448946836,351735813872,646956766742,1157359269036
%N A201374 Number of nX7 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.
%C A201374 Column 7 of A201375
%H A201374 R. H. Hardin, <a href="/A201374/b201374.txt">Table of n, a(n) for n = 1..210</a>
%F A201374 Empirical: a(n) = (1/64864800)*n^14 + (1/831600)*n^13 + (1643/59875200)*n^12 - (247/1995840)*n^11 - (5611/1360800)*n^10 + (61807/1814400)*n^9 + (11951/604800)*n^8 - (31427/30240)*n^7 + (10739983/2721600)*n^6 - (9433741/1814400)*n^5 + (252826879/29937600)*n^4 - (52757143/997920)*n^3 + (1595598461/10810800)*n^2 - (462725/2772)*n + 68
%e A201374 Some solutions for n=5
%e A201374 ..0..0..0..0..1..1..1....0..1..1..1..1..1..1....0..1..1..1..1..1..1
%e A201374 ..0..0..1..1..0..0..1....1..0..1..1..1..1..1....0..1..1..1..1..1..1
%e A201374 ..0..0..1..1..0..1..0....1..1..0..0..0..0..1....1..0..0..1..1..1..1
%e A201374 ..1..1..0..0..1..0..0....1..1..0..0..0..1..0....1..0..1..0..0..0..0
%e A201374 ..1..1..1..1..0..0..0....1..1..1..1..1..0..0....1..1..0..0..0..0..0
%K A201374 nonn
%O A201374 1,1
%A A201374 _R. H. Hardin_ Nov 30 2011