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A223954 Number of 7 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing. 1

%I

%S 128,2187,6869,12856,20275,31899,52532,89135,152495,259230,434069,

%T 712692,1145194,1800237,2769954,4175669,6174497,8966888,12805179,

%U 18003218,24947124,34107247,46051392,61459371,81138947,106043234,137289617

%N Number of 7 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

%C Row 7 of A223949.

%H R. H. Hardin, <a href="/A223954/b223954.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (4/315)*n^7 - (1/45)*n^6 + (34/45)*n^5 + (221/72)*n^4 + (4507/180)*n^3 + (42283/360)*n^2 + (53997/140)*n + 7577 for n>5.

%F Conjectures from _Colin Barker_, Aug 24 2018: (Start)

%F G.f.: x*(128 + 1163*x - 7043*x^2 + 11972*x^3 - 3753*x^4 - 9075*x^5 + 7046*x^6 + 2119*x^7 - 1755*x^8 - 2009*x^9 + 1146*x^10 + 346*x^11 - 221*x^12) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

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

%Y Cf. A223949.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 29 2013

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Last modified January 21 07:12 EST 2022. Contains 350473 sequences. (Running on oeis4.)