cp's OEIS Frontend

A224314 Number of 6Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%I A224314 #6 Jul 23 2025 05:06:10
%S A224314 729,69984,615481,2717759,9829605,33934344,118317987,416543502,
%T A224314 1454734611,4952178320,16233385381,50895787205,152210262323,
%U A224314 434202798968,1183383351150,3089018682146,7745205810204,18709904381707,43674432900423
%N A224314 Number of 6Xn 0..2 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C A224314 Row 6 of A224310
%H A224314 R. H. Hardin, <a href="/A224314/b224314.txt">Table of n, a(n) for n = 1..210</a>
%F A224314 Empirical: a(n) = (1/35608838483312640000)*n^24 - (1/989134402314240000)*n^23 + (29/340606281144729600)*n^22 - (53/37347179950080000)*n^21 + (22843/270322445352960000)*n^20 - (9467/35777970708480000)*n^19 + (662659/9959247986688000)*n^18 + (276971/2196892938240000)*n^17 + (3268463573/52725430517760000)*n^16 - (2963663/488198430720000)*n^15 + (9468406841/251073478656000)*n^14 - (84633169147/72425041920000)*n^13 + (487482300065231/17575143505920000)*n^12 - (1486260397277527/4393785876480000)*n^11 + (9918644607332189/5272543051776000)*n^10 + (43388314670213341/2196892938240000)*n^9 - (3089001310329622433/5335311421440000)*n^8 + (16161770203432180709/2000741783040000)*n^7 - (9131503366840338348499/106439462857728000)*n^6 + (11613280481413038257281/14783258730240000)*n^5 - (88365905776581806936999/14783258730240000)*n^4 + (4417617587739169133/127135008000)*n^3 - (377212760667401564861/2698531355520)*n^2 + (557689056867461/1615152)*n - 399418303 for n>12
%e A224314 Some solutions for n=3
%e A224314 ..0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..0..0....0..0..0
%e A224314 ..0..0..1....0..2..1....1..2..0....1..1..0....1..0..0....1..0..0....1..0..0
%e A224314 ..1..1..0....2..1..1....2..0..0....2..2..1....2..2..1....0..1..1....2..2..1
%e A224314 ..1..2..1....1..1..1....1..1..0....2..2..1....2..2..0....2..1..0....2..1..0
%e A224314 ..2..1..0....1..2..1....2..0..0....2..1..1....2..2..2....2..2..0....1..2..1
%e A224314 ..1..2..0....2..1..1....2..1..0....2..2..1....2..2..1....2..1..1....2..2..1
%K A224314 nonn
%O A224314 1,1
%A A224314 _R. H. Hardin_ Apr 03 2013