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A224173 T(n,k) = number of n X k 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.

%I A224173 #12 Mar 18 2025 16:05:11
%S A224173 4,16,10,50,100,20,130,684,400,35,296,3526,4739,1225,56,610,14751,
%T A224173 38561,22988,3136,84,1163,52591,242114,272130,87878,7056,120,2083,
%U A224173 165212,1253770,2335459,1460836,282372,14400,165,3544,468292,5588411,15925611
%N A224173 T(n,k) = number of n X k 0..3 arrays with rows, diagonals and antidiagonals unimodal and columns nondecreasing.
%H A224173 R. H. Hardin, <a href="/A224173/b224173.txt">Table of n, a(n) for n = 1..178</a>
%F A224173 Empirical: columns k=1..7 are polynomials of degree 3*k for n>0,0,0,3,6,9,12.
%F A224173 Empirical: rows n=1..5 are polynomials of degree 6*n for k>0,0,0,2,6.
%e A224173 Table starts:
%e A224173     4    16       50       130         296          610           1163
%e A224173    10   100      684      3526       14751        52591         165212
%e A224173    20   400     4739     38561      242114      1253770        5588411
%e A224173    35  1225    22988    272130     2335459     15925611       91494280
%e A224173    56  3136    87878   1460836    16625026    143558572     1012166273
%e A224173    84  7056   282372   6425876    95808564   1038484760     8857798353
%e A224173   120 14400   794220  24197608   468021427   6360047093    65713691148
%e A224173   165 27225  2010035  80350989  1994287334  33901838632   426013124302
%e A224173   220 48400  4668304 240416852  7568051210 160168789130  2451904991177
%e A224173   286 81796 10095924 658890738 25994968917 680269560125 12667946702827
%e A224173   ...
%e A224173 Some solutions for n=3 k=4
%e A224173 ..0..0..1..0....0..0..1..2....0..0..3..0....0..2..0..0....0..3..3..1
%e A224173 ..1..3..3..1....0..1..3..2....3..3..3..1....1..2..0..0....1..3..3..1
%e A224173 ..1..3..3..3....0..3..3..2....3..3..3..2....2..2..1..0....1..3..3..3
%Y A224173 Main diagonal is A224167.
%Y A224173 Columns 1..7 are A000292(n+1), A001249, A224168, A224169, A224170, A224171, A224172.
%Y A224173 Rows 1..7 are A223659, A223865, A224174, A224175, A224176, A224177, A224178.
%Y A224173 Cf. A223838.
%K A224173 nonn,tabl
%O A224173 1,1
%A A224173 _R. H. Hardin_, Mar 31 2013
%E A224173 Name corrected by _Andrew Howroyd_, Mar 18 2025