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Number of nX4 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.
1

%I #4 Nov 25 2016 15:17:47

%S 10,99,579,2650,10584,38848,134265,441349,1384443,4148373,11882640,

%T 32576006,85619948,216195769,525654868,1233512143,2800037121,

%U 6161774705,13172137674,27405600826,55592487870,110125213825,213350721015

%N Number of nX4 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.

%C Column 4 of A278676.

%H R. H. Hardin, <a href="/A278672/b278672.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/2432902008176640000)*n^20 + (1/16219346721177600)*n^19 + (113/25609494822912000)*n^18 + (19/94849980825600)*n^17 + (2719/418455797760000)*n^16 + (6689/41845579776000)*n^15 + (2324129/753220435968000)*n^14 + (1200247/25107347865600)*n^13 + (351438179/579400335360000)*n^12 + (1259149/195084288000)*n^11 + (254340707/4291854336000)*n^10 + (620067937/1287556300800)*n^9 + (236029006781/67251824640000)*n^8 + (715300432229/31384184832000)*n^7 + (12122971872241/94152554496000)*n^6 + (39838863931/69742632960)*n^5 + (192914714452637/111152321280000)*n^4 + (1979357687401/617512896000)*n^3 + (1837396540403/586637251200)*n^2 + (3628307/3023280)*n

%e Some solutions for n=4

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

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

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

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

%Y Cf. A278676.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 25 2016