A224745 T(n,k) is the number of (n+1) X (k+1) 0..1 matrices with each 2 X 2 permanent equal.

16, 38, 38, 89, 152, 89, 218, 565, 565, 218, 538, 2326, 2961, 2326, 538, 1349, 9554, 18257, 18257, 9554, 1349, 3410, 40297, 107665, 180546, 107665, 40297, 3410, 8690, 170754, 661569, 1644874, 1644874, 661569, 170754, 8690, 22273, 728996, 4028161

Offset

1,1

Comments

Table starts

....16.......38........89..........218............538.............1349

....38......152.......565.........2326...........9554............40297

....89......565......2961........18257.........107665...........661569

...218.....2326.....18257.......180546........1644874.........15845297

...538.....9554....107665......1644874.......21910274........316084673

..1349....40297....661569.....15845297......316084673.......6987578401

..3410...170754...4028161....149592266.....4390392346.....146736389761

..8690...728996..24772161...1430571502....62260133978....3168731910657

.22273..3120401.152077313..13614536577...873935026817...67464482340481

.57362.13387658.935846145.129950804946.12334039384018.1447369426794241

Links

R. H. Hardin, Table of n, a(n) for n = 1..544

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1) -6*a(n-2) -3*a(n-3) +7*a(n-4) -2*a(n-5)

k=2: a(n) = 7*a(n-1) -7*a(n-2) -34*a(n-3) +59*a(n-4) +27*a(n-5) -87*a(n-6) +36*a(n-7)

k=3: [order 9]

k=4: [order 13]

k=5: [order 20]

k=6: [order 34]

k=7: [order 55]

Example

Some solutions for n=3 k=4
..0..0..1..0..1....1..0..1..1..0....0..0..0..0..1....0..0..1..0..1
..0..0..0..0..0....1..0..0..0..0....0..0..1..0..1....0..0..1..0..1
..1..1..0..0..1....0..0..0..0..0....0..0..0..0..1....1..0..0..0..0
..0..0..0..0..0....1..1..1..0..1....1..0..1..0..1....1..0..0..0..1

Crossrefs

Sequence in context: A350288 A354473 A275186 * A070586 A166112 A224738

Adjacent sequences: A224742 A224743 A224744 * A224746 A224747 A224748

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 17 2013

Status

approved