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A223966 Number of 6Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A223966 #6 Jul 23 2025 04:43:05
%S A223966 4096,403104,5777663,37844037,163752797,556027700,1629022329,
%T A223966 4351046624,10953882109,26519610433,62472567689,144124515790,
%U A223966 326646013571,728132468716,1596498777021,3441674914130,7290815852670,15169818503342
%N A223966 Number of 6Xn 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A223966 Row 6 of A223961
%H A223966 R. H. Hardin, <a href="/A223966/b223966.txt">Table of n, a(n) for n = 1..210</a>
%F A223966 Empirical: a(n) = (1/73156608000)*n^18 + (1/2709504000)*n^17 + (3319/268240896000)*n^16 + (247579/871782912000)*n^15 + (1111849/193729536000)*n^14 + (3684553/35582976000)*n^13 + (658841977/402361344000)*n^12 + (521443357/22353408000)*n^11 + (7665391471/24385536000)*n^10 + (90826901857/24385536000)*n^9 + (333381059779/8128512000)*n^8 + (85061672873/217728000)*n^7 + (319642737999043/100590336000)*n^6 + (118989237432757/5588352000)*n^5 + (107614272658699/1862784000)*n^4 + (891088311042211/9081072000)*n^3 - (51719689062621/11211200)*n^2 + (1774047167507/360360)*n + 34898064 for n>11
%e A223966 Some solutions for n=3
%e A223966 ..0..0..0....0..0..2....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A223966 ..0..0..0....0..0..1....0..0..1....0..0..0....0..0..1....0..0..0....0..0..0
%e A223966 ..0..1..1....0..1..1....2..2..3....0..0..2....0..2..2....0..0..0....0..0..2
%e A223966 ..0..1..3....1..1..2....0..2..2....0..1..2....0..3..3....0..2..2....1..1..3
%e A223966 ..0..0..2....0..1..2....0..1..2....0..0..3....2..2..3....1..2..3....1..3..3
%e A223966 ..0..1..3....0..2..2....0..2..2....0..1..1....0..2..2....1..2..2....1..2..3
%K A223966 nonn
%O A223966 1,1
%A A223966 _R. H. Hardin_ Mar 29 2013