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A223989 Number of 4Xn 0..3 arrays with rows unimodal and columns nondecreasing.

%I A223989 #6 Jul 23 2025 04:46:42
%S A223989 35,1225,25410,358118,3770722,31585056,219861244,1312747586,
%T A223989 6885325482,32313530946,137690265950,539018300034,1957451099304,
%U A223989 6647631120056,21256016741041,64364748455011,185491652223781,510953158157281
%N A223989 Number of 4Xn 0..3 arrays with rows unimodal and columns nondecreasing.
%C A223989 Row 4 of A223987
%H A223989 R. H. Hardin, <a href="/A223989/b223989.txt">Table of n, a(n) for n = 1..210</a>
%F A223989 Empirical: a(n) = (1/2906843957821440000)*n^24 + (11/242236996485120000)*n^23 + (4897/1529252690853888000)*n^22 + (2857/19308746096640000)*n^21 + (973813/198604245565440000)*n^20 + (4751599/38617492193280000)*n^19 + (31125329/12804747411456000)*n^18 + (103519301/2667655710720000)*n^17 + (2190105457/4304116776960000)*n^16 + (4631351591/836911595520000)*n^15 + (151304213363/3012881743872000)*n^14 + (22821847439/59779399680000)*n^13 + (807436276336499/331416991825920000)*n^12 + (2978829718733/228248616960000)*n^11 + (12597307863407/215205838848000)*n^10 + (15260090056063/69742632960000)*n^9 + (21685072444447303/32011868528640000)*n^8 + (72957402495727/42343741440000)*n^7 + (108238697285043737/30411275102208000)*n^6 + (24731243901001117/4223788208640000)*n^5 + (1127736066113539/150849578880000)*n^4 + (8436170802181/1173274502400)*n^3 + (193928573189123/37104806138400)*n^2 + (1070454625/535422888)*n + 1
%e A223989 Some solutions for n=3
%e A223989 ..0..0..0....0..1..0....1..1..2....0..2..1....0..0..0....1..2..0....0..2..0
%e A223989 ..1..1..1....0..1..0....1..3..3....0..2..2....2..3..1....2..3..1....0..2..1
%e A223989 ..1..3..3....0..2..0....2..3..3....0..3..2....2..3..1....2..3..1....0..2..1
%e A223989 ..1..3..3....0..3..2....2..3..3....3..3..3....3..3..2....3..3..1....0..3..1
%K A223989 nonn
%O A223989 1,1
%A A223989 _R. H. Hardin_ Mar 30 2013