cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A189064 T(n,k)=Number of nXk binary arrays without the pattern 0 1 0 antidiagonally or horizontally.

Original entry on oeis.org

2, 4, 4, 7, 16, 8, 12, 49, 64, 16, 21, 144, 316, 256, 32, 37, 441, 1404, 2032, 1024, 64, 65, 1369, 6768, 13452, 13045, 4096, 128, 114, 4225, 33893, 99721, 128628, 83737, 16384, 256, 200, 12996, 167473, 795741, 1492864, 1228512, 537496, 65536, 512, 351, 40000
Offset: 1

Views

Author

R. H. Hardin Apr 16 2011

Keywords

Comments

Table starts
....2.......4.........7..........12............21..............37
....4......16........49.........144...........441............1369
....8......64.......316........1404..........6768...........33893
...16.....256......2032.......13452.........99721..........795741
...32....1024.....13045......128628.......1492864........19468046
...64....4096.....83737.....1228512......22289912.......477128662
..128...16384....537496....11733712.....333124565.....11711612310
..256...65536...3450100...112065936....4978704008....287687887135
..512..262144..22145617..1070316016...74410715409...7067105036501
.1024.1048576.142149013.10222334864.1112149145053.173620295413143

Examples

			Some solutions for 5X3
..1..0..0....0..0..1....1..0..1....0..0..1....0..0..1....1..1..1....1..1..0
..0..0..1....1..1..1....1..0..0....0..0..0....0..0..1....0..0..1....0..1..1
..1..1..1....0..1..1....0..0..1....0..0..0....1..1..0....1..0..0....1..1..1
..1..1..1....1..1..1....0..0..1....0..0..0....1..0..0....0..0..1....0..0..1
..1..0..0....0..0..1....0..1..1....1..0..1....0..0..0....1..1..0....0..1..1

Links

Crossrefs

Column 2 is Column 1 squared
Column 3 is A188868
Row 1 is A005251(n+3)
Row 2 is A188501

A189196 T(n,k)=Number of nXk binary arrays without the pattern 0 0 1 vertically or antidiagonally.

Original entry on oeis.org

2, 4, 4, 8, 16, 7, 16, 64, 49, 12, 32, 256, 316, 144, 20, 64, 1024, 2032, 1494, 400, 33, 128, 4096, 13045, 15326, 6446, 1089, 54, 256, 16384, 83737, 156564, 101628, 27170, 2916, 88, 512, 65536, 537496, 1598444, 1579664, 657028, 111778, 7744, 143, 1024, 262144
Offset: 1

Views

Author

R. H. Hardin Apr 18 2011

Keywords

Comments

Table starts
...2.....4.......8........16...........32.............64..............128
...4....16......64.......256.........1024...........4096............16384
...7....49.....316......2032........13045..........83737...........537496
..12...144....1494.....15326.......156564........1598444.........16316636
..20...400....6446....101628......1579664.......24496092........379515360
..33..1089...27170....657028.....15564047......367115337.......8646366042
..54..2916..111778...4109278....146936454.....5218915180.....184841938568
..88..7744..455376..25421672...1372985912....73539558380....3925306136096
.143.20449.1841116.155713446..12673978495..1021199649839...81929775932500
.232.53824.7415070.949556490.116484051544.14125557202206.1704770564043390

Examples

			Some solutions for 5X3
..1..1..1....0..1..1....0..1..1....0..0..0....0..1..1....0..0..1....1..0..1
..0..1..1....1..1..0....1..0..1....1..1..1....0..0..0....1..1..0....1..0..0
..1..0..0....0..1..1....1..0..0....1..1..0....0..1..1....0..1..1....1..0..1
..1..1..0....1..0..1....0..0..0....1..0..1....0..0..1....0..1..1....0..0..0
..1..0..0....0..0..1....0..0..0....0..1..1....0..0..0....0..1..0....0..0..0

Links

Crossrefs

Column 1 is A000071(n+3)
Column 2 is A188516
Row 3 is A188868

A223680 T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal.

Original entry on oeis.org

2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 316, 256, 32, 22, 256, 1118, 2032, 1024, 64, 29, 484, 3177, 9822, 13045, 4096, 128, 37, 841, 7745, 35509, 85663, 83737, 16384, 256, 46, 1369, 16857, 105995, 384009, 744272, 537496, 65536, 512, 56, 2116, 33615, 275775
Offset: 1

Views

Author

R. H. Hardin Mar 25 2013

Keywords

Comments

Table starts
....2.......4.........7.........11..........16...........22............29
....4......16........49........121.........256..........484...........841
....8......64.......316.......1118........3177.........7745.........16857
...16.....256......2032.......9822.......35509.......105995........275775
...32....1024.....13045......85663......384009......1363639.......4123210
...64....4096.....83737.....744272.....4106403.....17068664......58944337
..128...16384....537496....6458585....43632367....210660192.....821284360
..256...65536...3450100...56030742...462307835...2577807779...11265254628
..512..262144..22145617..486038270..4893189359..31402790284..152970187735
.1024.1048576.142149013.4215998078.51766786082.381690187059.2064772010660

Examples

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

Links

Crossrefs

Column 1 is A000079
Column 2 is A000302
Column 3 is A188868
Row 1 is A000124
Row 2 is A086601

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) = 7*a(n-1) -3*a(n-2) -5*a(n-3) +2*a(n-4)
k=4: [order 9]
k=5: [order 19]
k=6: [order 36]
k=7: [order 70]
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) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1
n=4: polynomial of degree 8
n=5: polynomial of degree 10 for n>2
n=6: polynomial of degree 12 for n>3
n=7: polynomial of degree 14 for n>4
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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