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A223876 T(n,k)=Number of nXk 0..3 arrays with rows, diagonals and antidiagonals unimodal.

%I A223876 #6 Jul 23 2025 04:37:29
%S A223876 4,16,16,50,256,64,130,2500,4096,256,296,16900,99223,65536,1024,610,
%T A223876 87616,1336985,3863372,1048576,4096,1163,372100,12520369,88682677,
%U A223876 152918517,16777216,16384,2083,1352569,90648289,1271992512,5941888105
%N A223876 T(n,k)=Number of nXk 0..3 arrays with rows, diagonals and antidiagonals unimodal.
%C A223876 Table starts
%C A223876 .......4............16................50..................130
%C A223876 ......16...........256..............2500................16900
%C A223876 ......64..........4096.............99223..............1336985
%C A223876 .....256.........65536...........3863372.............88682677
%C A223876 ....1024.......1048576.........152918517...........5941888105
%C A223876 ....4096......16777216........6066668157.........411716468431
%C A223876 ...16384.....268435456......240345697904.......28928809433978
%C A223876 ...65536....4294967296.....9519219712534.....2033941972287214
%C A223876 ..262144...68719476736...377068749332794...142745781634483746
%C A223876 .1048576.1099511627776.14936662560715369.10010372252279889400
%H A223876 R. H. Hardin, <a href="/A223876/b223876.txt">Table of n, a(n) for n = 1..97</a>
%F A223876 Empirical for column k:
%F A223876 k=1: a(n) = 4*a(n-1)
%F A223876 k=2: a(n) = 16*a(n-1)
%F A223876 k=3: [recurrence of order 28]
%F A223876 Empirical: rows n=1..4 are polynomials of degree 6*n for k>0,0,1,10
%e A223876 Some solutions for n=3 k=4
%e A223876 ..0..0..0..1....0..0..0..3....0..2..3..3....0..0..0..2....0..0..0..0
%e A223876 ..2..2..2..3....2..2..3..3....2..2..3..1....0..2..2..2....0..0..0..3
%e A223876 ..2..3..1..1....0..1..2..3....1..1..3..1....2..2..2..1....1..1..3..1
%Y A223876 Column 1 is A000302
%Y A223876 Column 2 is A001025
%Y A223876 Row 1 is A223659
%Y A223876 Row 2 is A223756
%K A223876 nonn,tabl
%O A223876 1,1
%A A223876 _R. H. Hardin_ Mar 28 2013