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A223669 T(n,k)=Number of nXk 0..1 arrays with rows, diagonals and antidiagonals unimodal 11
2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 292, 256, 32, 22, 256, 948, 1723, 1024, 64, 29, 484, 2527, 6454, 10327, 4096, 128, 37, 841, 5913, 18980, 44693, 61996, 16384, 256, 46, 1369, 12577, 49561, 136289, 321163, 371641, 65536, 512, 56, 2116, 24821, 119150 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
....2.......4........7........11.........16..........22..........29..........37
....4......16.......49.......121........256.........484.........841........1369
....8......64......292.......948.......2527........5913.......12577.......24821
...16.....256.....1723......6454......18980.......49561......119150......267643
...32....1024....10327.....44693.....136289......364959......920106.....2218590
...64....4096....61996....321163....1023339.....2715255.....6789502....16634224
..128...16384...371641...2343189....8052573....21347949....51831694...124050234
..256...65536..2227333..17087771...64796052...176196273...418107416...962697852
..512..262144.13350748.124218846..523162622..1493319998..3535212700..7863420454
.1024.1048576.80027347.901767902.4210122961.12752674920.30760010124.67121292946
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1)
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)
k=4: [order 23]
k=5: [order 93]
Empirical for row n:
n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1
n=3: a(n) = polynomial of degree 6 for n>1
n=4: a(n) = polynomial of degree 8 for n>6
n=5: a(n) = polynomial of degree 10 for n>12
n=6: a(n) = polynomial of degree 12 for n>20
EXAMPLE
Some solutions for n=4 k=4
..0..1..1..1....0..0..1..0....0..1..1..0....0..1..0..0....0..0..0..0
..0..1..1..0....1..1..1..1....1..1..1..0....0..1..1..0....0..0..0..0
..1..1..1..0....0..1..1..1....1..1..1..1....0..1..1..0....0..0..0..0
..0..0..0..0....0..0..1..0....1..1..1..0....0..0..0..1....1..1..1..1
CROSSREFS
Column 1 is A000079
Column 2 is A000302
Column 3 is A188748
Row 1 is A000124
Row 2 is A086601
Sequence in context: A181224 A188567 A262274 * A223680 A189264 A188992
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Mar 25 2013
STATUS
approved

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Last modified July 19 17:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)