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A224148 Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1

%I

%S 5,25,92,272,691,1573,3296,6472,12058,21506,36961,61517,99542,157084,

%T 242371,366419,543763,793327,1139450,1613086,2253197,3108359,4238602,

%U 5717506,7634576,10097920,13237255,17207267,22191352,28405766,36104213

%N Number of 4 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Row 4 of A224146.

%H R. H. Hardin, <a href="/A224148/b224148.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (1/192)*n^6 + (1/16)*n^5 + (223/640)*n^4 + (149/160)*n^3 + (3319/2016)*n^2 + (169/168)*n + 1.

%F Conjectures from _Colin Barker_, Aug 28 2018: (Start)

%F G.f.: x*(5 - 20*x + 47*x^2 - 76*x^3 + 85*x^4 - 62*x^5 + 29*x^6 - 8*x^7 + x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=3:

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

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

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

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

%Y Cf. A224146.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2013

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Last modified May 22 02:18 EDT 2022. Contains 353933 sequences. (Running on oeis4.)