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A223804 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal.

%I A223804 #6 Jul 23 2025 04:32:34
%S A223804 1024,1048576,210163664,13602542576,453578376041,9658691177678,
%T A223804 147492079608804,1738265364563074,16624933432537046,
%U A223804 133772722680020893,930338345848608947,5709392263061431701,31428574139042436485
%N A223804 Number of 5Xn 0..3 arrays with rows and antidiagonals unimodal.
%C A223804 Row 5 of A223801
%H A223804 R. H. Hardin, <a href="/A223804/b223804.txt">Table of n, a(n) for n = 1..152</a>
%F A223804 Empirical: a(n) = (12185409283/15043832793341144432640000000)*n^30 + (76296730104643/884176199373970195454361600000)*n^29 + (371907650782571/65333216702510112964608000000)*n^28 + (1151102366842559/4355547780167340864307200000)*n^27 + (338234821790386273/36296231501394507202560000000)*n^26 + (357033935267827/1378774226073865420800000)*n^25 + (13631151365462522107/2345294958551645080780800000)*n^24 + (16740679506000614867/156352997236776338718720000)*n^23 + (119233024700630228357/72835247159988977664000000)*n^22 + (263813261261433287/12612164010387701760000)*n^21 + (64065941370817311811/285628420235250892800000)*n^20 + (8076987180619121371/3996447032098160640000)*n^19 + (5334961705848505741485791/348842499555736682496000000)*n^18 + (450858411768010052623451/4651233327409822433280000)*n^17 + (300491370965924162197759/586289915219725516800000)*n^16 + (17563968862511001347771/7817198869596340224000)*n^15 + (134531017813019228073534643/16611547597892222976000000)*n^14 + (33668222196298965216433/1419790392982241280000)*n^13 + (224429158876824166363763453/4025105764104654028800000)*n^12 + (12074189473194325363982201/115874256845437009920000)*n^11 + (10894534329021783625843566583/68283044212489666560000000)*n^10 + (44842282464981860911345889/227610147374965555200000)*n^9 + (500341840567104079760229311/2908351883124559872000000)*n^8 - (6956889324683760951709681/12118132846352332800000)*n^7 - (22335181829123680152688619197/9189584075150519040000000)*n^6 - (486619909336332713379638689/61263893834336793600000)*n^5 - (1635897124538888506513/525329221697280000)*n^4 - (35225574821544661546673/7293320694563904000)*n^3 + (382682859390107193527/9647249595984000)*n^2 - (11221241883754589/465817912560)*n - 377 for n>2
%e A223804 Some solutions for n=3
%e A223804 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A223804 ..0..0..0....0..2..0....0..0..0....0..0..0....0..0..0....0..2..0....0..2..0
%e A223804 ..2..2..1....1..2..0....0..0..0....1..0..0....2..0..0....3..2..2....0..2..1
%e A223804 ..3..1..1....1..3..2....2..3..2....3..3..0....0..2..1....2..2..2....1..3..3
%e A223804 ..1..2..0....3..1..0....1..3..2....3..0..0....3..1..1....1..1..1....2..2..1
%K A223804 nonn
%O A223804 1,1
%A A223804 _R. H. Hardin_ Mar 27 2013