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A223639 Number of n X 3 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal. 1

%I

%S 7,49,218,726,2014,4904,10797,21917,41601,74635,127636,209480,331776,

%T 509386,760991,1109703,1583723,2217045,3050206,4131082,5515730,

%U 7269276,9466849,12194561,15550533,19645967,24606264,30572188,37701076,46168094

%N Number of n X 3 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

%C Column 3 of A223644.

%H R. H. Hardin, <a href="/A223639/b223639.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (23/360)*n^6 - (3/40)*n^5 + (31/18)*n^4 + (5/8)*n^3 + (1517/360)*n^2 - (51/20)*n + 3.

%F Conjectures from _Colin Barker_, Aug 22 2018: (Start)

%F G.f.: x*(7 + 22*x^2 - 16*x^3 + 40*x^4 - 10*x^5 + 3*x^6) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A223644.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 24 2013

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Last modified January 26 13:09 EST 2022. Contains 350598 sequences. (Running on oeis4.)