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A223792 Number of 5Xn 0..2 arrays with rows, diagonals and antidiagonals unimodal.

%I A223792 #6 Jul 23 2025 04:31:17
%S A223792 243,59049,2703137,39387861,343454446,2226551034,11992802966,
%T A223792 57005353680,246381084601,983376748824,3659208824870,12782748762891,
%U A223792 42154099154095,131837732493171,392589737558511,1116957062770205,3045559149318525
%N A223792 Number of 5Xn 0..2 arrays with rows, diagonals and antidiagonals unimodal.
%C A223792 Row 5 of A223789
%H A223792 R. H. Hardin, <a href="/A223792/b223792.txt">Table of n, a(n) for n = 1..103</a>
%F A223792 Empirical: a(n) = (63370093/405483668029440000)*n^20 - (268330757/121645100408832000)*n^19 + (43030249/328326856704000)*n^18 - (5473141/17072996548608)*n^17 - (2435352473/69742632960000)*n^16 + (170082680039/62768369664000)*n^15 - (9040480367419/125536739328000)*n^14 + (52864434956213/37661021798400)*n^13 - (1853752694469833/96566722560000)*n^12 + (2309334348058723/9656672256000)*n^11 - (7549354911696211/2145927168000)*n^10 + (117446496741518107/1931334451200)*n^9 - (140966223776288630033/156920924160000)*n^8 + (91382436096707306951/9415255449600)*n^7 - (86620685132489250907/1207084032000)*n^6 + (58712885643301237303/174356582400)*n^5 - (288444549825617915291/343062720000)*n^4 + (167215711426064855461/308756448000)*n^3 - (1138388070473741029/24443218800)*n^2 + (154082848393578809/16628040)*n - 14652081349 for n>15
%e A223792 Some solutions for n=3
%e A223792 ..0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....0..0..1....0..0..0
%e A223792 ..2..0..0....2..0..0....0..0..2....0..1..0....1..1..1....0..1..0....1..0..0
%e A223792 ..0..2..2....0..1..1....0..0..0....0..1..0....0..1..1....0..1..1....0..1..1
%e A223792 ..1..2..0....0..1..0....0..0..2....0..2..0....0..1..2....0..2..2....1..1..1
%e A223792 ..0..1..1....2..1..0....1..2..2....2..2..2....1..2..0....0..2..0....0..0..0
%K A223792 nonn
%O A223792 1,1
%A A223792 _R. H. Hardin_ Mar 27 2013