A224354 - OEIS

%I #7 Aug 29 2018 15:24:39

%S 27,216,788,2321,5840,13052,26610,50423,90012,152912,249120,391589,

%T 596768,885188,1282094,1818123,2530028,3461448,4663724,6196761,

%U 8129936,10543052,13527338,17186495,21637788,27013184,33460536,41144813,50249376

%N Number of 3 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

%C Row 3 of A224353.

%H R. H. Hardin, <a href="/A224354/b224354.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (23/360)*n^6 + (19/40)*n^5 + (235/72)*n^4 + (61/8)*n^3 + (1921/180)*n^2 + (189/10)*n + 3 for n>1.

%F Conjectures from _Colin Barker_, Aug 29 2018: (Start)

%F G.f.: x*(27 + 27*x - 157*x^2 + 396*x^3 - 474*x^4 + 326*x^5 - 116*x^6 + 17*x^7) / (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>8.

%F (End)

%e Some solutions for n=3:

%e ..0..0..1....1..1..2....2..2..2....0..2..2....0..1..1....1..1..1....0..1..2

%e ..1..1..2....1..1..2....2..2..2....1..1..1....1..1..2....1..1..2....1..1..1

%e ..1..2..2....0..1..1....1..1..2....1..1..1....0..0..0....0..2..2....1..1..2

%Y Cf. A224353.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 04 2013