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A224023 Number of nX7 0..3 arrays with rows nondecreasing and antidiagonals unimodal.

%I A224023 #6 Jul 23 2025 04:53:21
%S A224023 120,14400,1074167,60614473,2903448338,126168072638,5173325036371,
%T A224023 204938686276996,7955563596264227,305205052747757176,
%U A224023 11629551123798091509,441423012052721410018,16718581835762003857099
%N A224023 Number of nX7 0..3 arrays with rows nondecreasing and antidiagonals unimodal.
%C A224023 Column 7 of A224024
%H A224023 R. H. Hardin, <a href="/A224023/b224023.txt">Table of n, a(n) for n = 1..210</a>
%F A224023 Empirical: a(n) = 120*a(n-1) -6060*a(n-2) +173316*a(n-3) -3172287*a(n-4) +39656548*a(n-5) -352443358*a(n-6) +2297379936*a(n-7) -11353877196*a(n-8) +45067977530*a(n-9) -163575910944*a(n-10) +627001572604*a(n-11) -2683978430932*a(n-12) +10780238513518*a(n-13) -32948873206590*a(n-14) +77959459244560*a(n-15) -153434141519476*a(n-16) +1059262494852896*a(n-17) -2694841466898608*a(n-18) +12219509145685508*a(n-19) +11985467868644368*a(n-20) +94047496662754280*a(n-21) +94835829721618640*a(n-22) +1050524403777918000*a(n-23) +2113714471975471104*a(n-24) +5481174460069822848*a(n-25) +10535537672809153264*a(n-26) +27173919094636341472*a(n-27) +47704013358770735568*a(n-28) +67212912534846684448*a(n-29) +62342889733184689824*a(n-30) +49243871592902490976*a(n-31) +27263322225301218304*a(n-32) +12918679041553050240*a(n-33) +2921299068148297728*a(n-34) +856946059741420288*a(n-35) -327218428029860352*a(n-36) -16665963801149440*a(n-37) -24912329585756160*a(n-38) +4712255288340480*a(n-39) +807198452121600*a(n-40) +68097422131200*a(n-41)
%e A224023 Some solutions for n=3
%e A224023 ..0..0..0..1..1..1..2....0..0..0..0..1..2..3....0..0..0..0..1..3..3
%e A224023 ..0..0..0..0..1..2..3....0..0..2..2..2..3..3....0..0..0..0..0..0..0
%e A224023 ..0..0..0..2..2..3..3....0..1..2..2..3..3..3....0..0..0..0..0..0..3
%K A224023 nonn
%O A224023 1,1
%A A224023 _R. H. Hardin_ Mar 30 2013