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 1-5 of 5 results.

A208028 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 102, 81, 13, 26, 256, 378, 279, 169, 19, 42, 676, 1260, 1377, 741, 361, 28, 68, 1764, 4374, 5895, 4823, 1995, 784, 41, 110, 4624, 14946, 26685, 26845, 17119, 5404, 1681, 60, 178, 12100, 51384, 118179, 158847, 123709
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Table starts
..2....4.....6.....10......16.......26........42.........68.........110
..4...16....36....100.....256......676......1764.......4624.......12100
..6...36...102....378....1260.....4374.....14946......51384......176238
..9...81...279...1377....5895....26685....118179.....527913.....2350215
.13..169...741...4823...26845...158847....917293....5349227....31070195
.19..361..1995..17119..123709...955073...7184755...54606513...413322903
.28..784..5404..61292..574560..5788524..56728924..561913408..5542832148
.41.1681.14555.218243.2652823.34901455.445530887.5753550295.73969794325

Examples

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

Links

Crossrefs

Column 1 is A000930(n+3)
Column 2 is A207170
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A060521

A207808 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 10, 16, 100, 102, 100, 16, 26, 256, 378, 370, 256, 26, 42, 676, 1260, 1970, 1232, 676, 42, 68, 1764, 4374, 9040, 9168, 4238, 1764, 68, 110, 4624, 14946, 43990, 57184, 44538, 14406, 4624, 110, 178, 12100, 51384, 209050, 382288
Offset: 1

Views

Author

R. H. Hardin Feb 20 2012

Keywords

Comments

Table starts
..2....4.....6......10.......16........26.........42..........68...........110
..4...16....36.....100......256.......676.......1764........4624.........12100
..6...36...102.....378.....1260......4374......14946.......51384........176238
.10..100...370....1970.....9040.....43990.....209050.....1002960.......4793390
.16..256..1232....9168....57184....382288....2485392....16340928.....106947696
.26..676..4238...44538...379444...3511534...31431114...285153752....2572767886
.42.1764.14406..212814..2472540..31569510..388134978..4844843724...60105117534
.68.4624.49164.1022652.16206848.285774964.4829044276.82999241712.1416863447084

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207249
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A060521

A208287 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 8, 16, 100, 102, 64, 10, 26, 256, 378, 216, 100, 12, 42, 676, 1260, 984, 390, 144, 14, 68, 1764, 4374, 3984, 2090, 636, 196, 16, 110, 4624, 14946, 16872, 9900, 3900, 966, 256, 18, 178, 12100, 51384, 70216, 49130, 21096, 6650, 1392
Offset: 1

Views

Author

R. H. Hardin Feb 25 2012

Keywords

Comments

Table starts
..2...4....6....10....16.....26......42.......68.......110........178
..4..16...36...100...256....676....1764.....4624.....12100......31684
..6..36..102...378..1260...4374...14946....51384....176238.....605022
..8..64..216...984..3984..16872...70216...294192...1229400....5142728
.10.100..390..2090..9900..49130..239490..1175440...5754050...28195750
.12.144..636..3900.21096.119580..665892..3733080..20874900..116842500
.14.196..966..6650.40376.256774.1604862.10095932..63357434..397965218
.16.256.1392.10608.71360.502416.3478160.24229696.168399632.1171405168

Examples

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

Links

Crossrefs

Column 2 is A016742
Column 3 is A086113
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A060521

Formula

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 2*n^3 + 6*n^2 - 2*n
k=4: a(n) = (4/3)*n^4 + 10*n^3 + (2/3)*n^2 - 2*n
k=5: a(n) = (5/6)*n^5 + 9*n^4 + (91/6)*n^3 - 9*n^2
k=6: a(n) = (8/15)*n^6 + (23/3)*n^5 + (82/3)*n^4 + (1/3)*n^3 - (178/15)*n^2 + 2*n
k=7: a(n) = (61/180)*n^7 + (121/20)*n^6 + (1157/36)*n^5 + (425/12)*n^4 - (2923/90)*n^3 - (22/15)*n^2 + 2*n

A208420 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 102, 81, 13, 26, 256, 378, 261, 169, 18, 42, 676, 1260, 1269, 611, 324, 25, 68, 1764, 4374, 5139, 3835, 1278, 625, 34, 110, 4624, 14946, 22509, 18395, 10098, 2625, 1156, 46, 178, 12100, 51384, 95265, 100113, 55404, 26375
Offset: 1

Views

Author

R. H. Hardin Feb 26 2012

Keywords

Comments

Table starts
..2....4....6....10.....16......26.......42........68........110.........178
..4...16...36...100....256.....676.....1764......4624......12100.......31684
..6...36..102...378...1260....4374....14946.....51384.....176238......605022
..9...81..261..1269...5139...22509....95265....409239....1746639.....7475751
.13..169..611..3835..18395..100113...512525...2702193...14044303....73505289
.18..324.1278.10098..55404..365094..2187162..13759164...84389022...524422458
.25..625.2625.26375.161975.1297475..8948825..67061525..479579725..3521095775
.34.1156.5134.65178.440436.4270706.33334858.295643872.2428615750.20882937190

Examples

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

Links

Crossrefs

Column 1 is A171861(n+1)
Column 2 is A207025
Column 3 is A207903
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A060521

A203407 T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 000 and 111 in rows and columns.

Original entry on oeis.org

102, 378, 378, 1260, 2030, 1260, 4374, 9484, 9484, 4374, 14946, 46746, 60232, 46746, 14946, 51384, 225654, 408432, 408432, 225654, 51384, 176238, 1098136, 2699464, 3858082, 2699464, 1098136, 176238, 605022, 5327258, 18021052, 35345798
Offset: 1

Views

Author

R. H. Hardin Jan 01 2012

Keywords

Comments

Table starts
.....102.......378........1260..........4374...........14946............51384
.....378......2030........9484.........46746..........225654..........1098136
....1260......9484.......60232........408432.........2699464.........18021052
....4374.....46746......408432.......3858082........35345798........327725888
...14946....225654.....2699464......35345798.......446672706.......5723980832
...51384...1098136....18021052.....327725888......5723980832.....101578277384
..176238...5327258...119835492....3024430930.....72950746702....1791372199364
..605022..25875154...798096928...27962750194....931753350314...31670053199428
.2076288.125619088..5312099836..258345914196..11890606324592..559357046066336
.7126302.609970274.35365379640.2387518651034.151793100413822.9883171811276912

Examples

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

Links

Crossrefs

Column 1 is A060521(n+2)
Column 2 is A060522(n+2)
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.