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A223669 T(n,k)=Number of nXk 0..1 arrays with rows, diagonals and antidiagonals unimodal.

%I A223669 #6 Jul 23 2025 04:22:22
%S A223669 2,4,4,7,16,8,11,49,64,16,16,121,292,256,32,22,256,948,1723,1024,64,
%T A223669 29,484,2527,6454,10327,4096,128,37,841,5913,18980,44693,61996,16384,
%U A223669 256,46,1369,12577,49561,136289,321163,371641,65536,512,56,2116,24821,119150
%N A223669 T(n,k)=Number of nXk 0..1 arrays with rows, diagonals and antidiagonals unimodal.
%C A223669 Table starts
%C A223669 ....2.......4........7........11.........16..........22..........29..........37
%C A223669 ....4......16.......49.......121........256.........484.........841........1369
%C A223669 ....8......64......292.......948.......2527........5913.......12577.......24821
%C A223669 ...16.....256.....1723......6454......18980.......49561......119150......267643
%C A223669 ...32....1024....10327.....44693.....136289......364959......920106.....2218590
%C A223669 ...64....4096....61996....321163....1023339.....2715255.....6789502....16634224
%C A223669 ..128...16384...371641...2343189....8052573....21347949....51831694...124050234
%C A223669 ..256...65536..2227333..17087771...64796052...176196273...418107416...962697852
%C A223669 ..512..262144.13350748.124218846..523162622..1493319998..3535212700..7863420454
%C A223669 .1024.1048576.80027347.901767902.4210122961.12752674920.30760010124.67121292946
%H A223669 R. H. Hardin, <a href="/A223669/b223669.txt">Table of n, a(n) for n = 1..179</a>
%F A223669 Empirical for column k:
%F A223669 k=1: a(n) = 2*a(n-1)
%F A223669 k=2: a(n) = 4*a(n-1)
%F A223669 k=3: a(n) = 6*a(n-1) -2*a(n-2) +11*a(n-3) +10*a(n-4) -30*a(n-5) -12*a(n-6)
%F A223669 k=4: [order 23]
%F A223669 k=5: [order 93]
%F A223669 Empirical for row n:
%F A223669 n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
%F A223669 n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1
%F A223669 n=3: a(n) = polynomial of degree 6 for n>1
%F A223669 n=4: a(n) = polynomial of degree 8 for n>6
%F A223669 n=5: a(n) = polynomial of degree 10 for n>12
%F A223669 n=6: a(n) = polynomial of degree 12 for n>20
%e A223669 Some solutions for n=4 k=4
%e A223669 ..0..1..1..1....0..0..1..0....0..1..1..0....0..1..0..0....0..0..0..0
%e A223669 ..0..1..1..0....1..1..1..1....1..1..1..0....0..1..1..0....0..0..0..0
%e A223669 ..1..1..1..0....0..1..1..1....1..1..1..1....0..1..1..0....0..0..0..0
%e A223669 ..0..0..0..0....0..0..1..0....1..1..1..0....0..0..0..1....1..1..1..1
%Y A223669 Column 1 is A000079
%Y A223669 Column 2 is A000302
%Y A223669 Column 3 is A188748
%Y A223669 Row 1 is A000124
%Y A223669 Row 2 is A086601
%K A223669 nonn,tabl
%O A223669 1,1
%A A223669 _R. H. Hardin_ Mar 25 2013