A224002 - OEIS

%I #8 Aug 25 2018 15:41:25

%S 81,793,2980,7927,17929,36845,71061,130767,231730,397675,663404,

%T 1078800,1713877,2665051,4062821,6081063,8948154,12960157,18496312,

%U 26037092,36185097,49689073,67471357,90659063,120619338,158999031,207769132

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

%C Row 4 of A223999.

%H R. H. Hardin, <a href="/A224002/b224002.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/2880)*n^8 + (1/180)*n^7 + (25/288)*n^6 + (169/180)*n^5 + (18649/2880)*n^4 + (4247/90)*n^3 + (2719/16)*n^2 - (6649/30)*n - 17 for n>4.

%F Conjectures from _Colin Barker_, Aug 25 2018: (Start)

%F G.f.: x*(81 + 64*x - 1241*x^2 + 2851*x^3 - 2540*x^4 + 248*x^5 + 1398*x^6 - 1380*x^7 + 796*x^8 - 347*x^9 + 88*x^10 - x^11 - 3*x^12) / (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>13.

%F (End)

%e Some solutions for n=3:

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

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

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

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

%Y Cf. A223999.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 30 2013