A223669 - OEIS

%I #4 Mar 25 2013 09:36:40

%S 2,4,4,7,16,8,11,49,64,16,16,121,292,256,32,22,256,948,1723,1024,64,

%T 29,484,2527,6454,10327,4096,128,37,841,5913,18980,44693,61996,16384,

%U 256,46,1369,12577,49561,136289,321163,371641,65536,512,56,2116,24821,119150

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

%C Table starts

%C ....2.......4........7........11.........16..........22..........29..........37

%C ....4......16.......49.......121........256.........484.........841........1369

%C ....8......64......292.......948.......2527........5913.......12577.......24821

%C ...16.....256.....1723......6454......18980.......49561......119150......267643

%C ...32....1024....10327.....44693.....136289......364959......920106.....2218590

%C ...64....4096....61996....321163....1023339.....2715255.....6789502....16634224

%C ..128...16384...371641...2343189....8052573....21347949....51831694...124050234

%C ..256...65536..2227333..17087771...64796052...176196273...418107416...962697852

%C ..512..262144.13350748.124218846..523162622..1493319998..3535212700..7863420454

%C .1024.1048576.80027347.901767902.4210122961.12752674920.30760010124.67121292946

%H R. H. Hardin, <a href="/A223669/b223669.txt">Table of n, a(n) for n = 1..179</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 4*a(n-1)

%F 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 k=4: [order 23]

%F k=5: [order 93]

%F Empirical for row n:

%F n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1

%F n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1

%F n=3: a(n) = polynomial of degree 6 for n>1

%F n=4: a(n) = polynomial of degree 8 for n>6

%F n=5: a(n) = polynomial of degree 10 for n>12

%F n=6: a(n) = polynomial of degree 12 for n>20

%e Some solutions for n=4 k=4

%e ..0..1..1..1....0..0..1..0....0..1..1..0....0..1..0..0....0..0..0..0

%e ..0..1..1..0....1..1..1..1....1..1..1..0....0..1..1..0....0..0..0..0

%e ..1..1..1..0....0..1..1..1....1..1..1..1....0..1..1..0....0..0..0..0

%e ..0..0..0..0....0..0..1..0....1..1..1..0....0..0..0..1....1..1..1..1

%Y Column 1 is A000079

%Y Column 2 is A000302

%Y Column 3 is A188748

%Y Row 1 is A000124

%Y Row 2 is A086601

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 25 2013