A223914 - OEIS

%I #8 Aug 24 2018 04:37:54

%S 46,548,3311,14123,48182,139925,359344,837243,1802306,3633256,6929795,

%T 12606425,22013660,37091549,60560840,96157525,148916916,225513812,

%U 334665727,487606559,698638490,985770317,1371450824,1883406215

%N Number of n X 4 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Column 4 of A223918.

%H R. H. Hardin, <a href="/A223914/b223914.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (41/4032)*n^8 + (41/336)*n^7 + (1277/1440)*n^6 + (953/240)*n^5 + (5363/576)*n^4 + (35/2)*n^3 + (28211/1680)*n^2 - (223/140)*n - 7 for n>1.

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

%F G.f.: x*(46 + 134*x + 35*x^2 + 188*x^3 + 35*x^4 - 157*x^5 + 241*x^6 - 153*x^7 + 47*x^8 - 6*x^9) / (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>10.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A223918.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 29 2013