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.

Previous Showing 11-15 of 15 results.

A207938 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 14, 81, 98, 64, 10, 22, 196, 271, 200, 100, 12, 35, 484, 844, 643, 350, 144, 14, 56, 1225, 2706, 2422, 1271, 556, 196, 16, 90, 3136, 8977, 9430, 5594, 2239, 826, 256, 18, 145, 8100, 30168, 38207, 25490, 11256, 3641, 1168, 324, 20, 234
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2...4....6....9....14.....22......35.......56.......90.......145........234
..4..16...36...81...196....484....1225.....3136.....8100.....21025......54756
..6..36...98..271...844...2706....8977....30168...102384....349069....1193648
..8..64..200..643..2422...9430...38207...156792...649758...2703377...11276024
.10.100..350.1271..5594..25490..121313...584386..2841676..13864995...67793828
.12.144..556.2239.11256..58602..319439..1760946..9794226..54631117..305277128
.14.196..826.3641.20568.120276..737575..4570122.28555126.178852957.1121957980
.16.256.1168.5581.34986.226850.1544037.10609482.73474400.509887759.3543126698

Examples

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

Links

Crossrefs

Column 1 is A004275(n+1)
Column 2 is A016742
Column 3 is A207106
Column 4 is A207107
Row 1 is A001611(n+2)
Row 2 is A207436

A208840 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 78, 81, 14, 26, 256, 282, 171, 196, 22, 42, 676, 768, 855, 406, 484, 35, 68, 1764, 2430, 2421, 3010, 990, 1225, 56, 110, 4624, 7086, 9801, 8736, 11242, 2485, 3136, 90, 178, 12100, 21588, 31419, 49126, 33088, 44275
Offset: 1

Views

Author

R. H. Hardin Mar 01 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...78....282....768.....2430.....7086.....21588......64230......193554
..9...81..171....855...2421.....9801....31419....116919.....394965.....1419849
.14..196..406...3010...8736....49126...169974....833364....3166030....14462714
.22..484..990..11242..33088...272206...992574...6800596...28280758...173714530
.35.1225.2485..44275.131355..1644265..6206445..62470275..277136755..2417186345
.56.3136.6328.179032.533568.10399480.40122936.613538688.2842543480.36689660504

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Column 3 is A208103
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A208689

Formula

Empirical for row n:
n=1: a(k)=a(k-1)+a(k-2)
n=2: a(k)=2*a(k-1)+2*a(k-2)-a(k-3)
n=3: a(k)=2*a(k-1)+4*a(k-2)-3*a(k-3)
n=4: a(k)=2*a(k-1)+7*a(k-2)-6*a(k-3)
n=5: a(k)=2*a(k-1)+12*a(k-2)-11*a(k-3)
n=6: a(k)=2*a(k-1)+20*a(k-2)-19*a(k-3)
n=7: a(k)=2*a(k-1)+33*a(k-2)-32*a(k-3)

A209650 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 8, 14, 81, 102, 64, 10, 22, 196, 270, 216, 100, 12, 35, 484, 798, 630, 390, 144, 14, 56, 1225, 2354, 2156, 1215, 636, 196, 16, 90, 3136, 7210, 7128, 4690, 2079, 966, 256, 18, 145, 8100, 22232, 24990, 16830, 8904, 3276, 1392, 324, 20, 234
Offset: 1

Views

Author

R. H. Hardin Mar 11 2012

Keywords

Comments

Table starts
..2...4....6....9....14.....22.....35......56.......90......145.......234
..4..16...36...81...196....484...1225....3136.....8100....21025.....54756
..6..36..102..270...798...2354...7210...22232....69570...218950....693810
..8..64..216..630..2156...7128..24990...87136...311040..1112150...4018716
.10.100..390.1215..4690..16830..65765..251160...994050..3911375..15639390
.12.144..636.2079..8904..34012.145775..597856..2579940.10954895..47622744
.14.196..966.3276.15386..61754.287140.1247736..5805450.26247900.122620446
.16.256.1392.4860.24808.103664.518700.2364992.11769120.56106300.279344520

Examples

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

Links

Crossrefs

Column 2 is A016742
Column 3 is A086113
Row 1 is A001611(n+2)
Row 2 is A207436
Row 3 is A207747

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) = 9*n^3 + (9/2)*n^2 - (9/2)*n
k=5: a(n) = (7/2)*n^4 + 21*n^3 - (7/2)*n^2 - 7*n
k=6: a(n) = 22*n^4 + (88/3)*n^3 - 22*n^2 - (22/3)*n
k=7: a(n) = 7*n^5 + 70*n^4 + (35/3)*n^3 - (105/2)*n^2 - (7/6)*n

A208698 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 14, 81, 98, 100, 16, 22, 196, 271, 358, 256, 26, 35, 484, 844, 1309, 1152, 676, 42, 56, 1225, 2706, 5524, 5371, 3910, 1764, 68, 90, 3136, 8977, 24086, 30160, 23637, 12994, 4624, 110, 145, 8100, 30168, 109599, 177488, 177872
Offset: 1

Views

Author

R. H. Hardin Mar 01 2012

Keywords

Comments

Table starts
..2....4.....6......9......14.......22.........35..........56...........90
..4...16....36.....81.....196......484.......1225........3136.........8100
..6...36....98....271.....844.....2706.......8977.......30168.......102384
.10..100...358...1309....5524....24086.....109599......506870......2376964
.16..256..1152...5371...30160...177488....1103081.....6990922.....45002090
.26..676..3910..23637..177872..1415508...12014735...104356568....923279444
.42.1764.12994.101069.1016258.10934750..126827983..1510509752..18362140414
.68.4624.43596.438103.5893862.85697362.1356513169.22125222702.369223577680

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207462
Column 4 is A207914
Row 1 is A001611(n+2)
Row 2 is A207436
Row 3 is A207939

A208007 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 1 1 and 1 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 14, 81, 92, 81, 14, 22, 196, 221, 221, 196, 22, 35, 484, 618, 536, 618, 484, 35, 56, 1225, 1690, 1711, 1711, 1690, 1225, 56, 90, 3136, 4861, 4993, 7016, 4993, 4861, 3136, 90, 145, 8100, 13900, 16742, 24512, 24512, 16742, 13900
Offset: 1

Views

Author

R. H. Hardin Feb 22 2012

Keywords

Comments

Table starts
..2....4.....6.....9.....14......22.......35........56........90........145
..4...16....36....81....196.....484.....1225......3136......8100......21025
..6...36....92...221....618....1690.....4861.....13900.....40452.....117717
..9...81...221...536...1711....4993....16742.....53411....182247.....608142
.14..196...618..1711...7016...24512...106503....411848...1787438....7238503
.22..484..1690..4993..24512...90232...486443...2001968..10846870...47911153
.35.1225..4861.16742.106503..486443..3569728..18874239.139219755..803098636
.56.3136.13900.53411.411848.2001968.18874239.101519408.989521860.5706548155

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Column 3 is A207559
Previous Showing 11-15 of 15 results.

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

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