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 1-10 of 17 results. Next

A231764 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal, diagonal and antidiagonal neighbors equal to one.

Original entry on oeis.org

9, 33, 16, 100, 136, 36, 315, 625, 660, 81, 961, 2976, 5041, 3213, 169, 3024, 15625, 38160, 40000, 14989, 361, 9409, 84817, 356409, 493695, 303601, 70927, 784, 29319, 440896, 3453471, 8231161, 5879679, 2353156, 338352, 1681, 91204, 2280000
Offset: 1

Views

Author

R. H. Hardin, Nov 13 2013

Keywords

Comments

Table starts
....9.......33........100...........315.............961...............3024
...16......136........625..........2976...........15625..............84817
...36......660.......5041.........38160..........356409............3453471
...81.....3213......40000........493695.........8231161..........143424652
..169....14989.....303601.......5879679.......175642009.........5493044921
..361....70927....2353156......71884125......3855664836.......216545491864
..784...338352...18318400.....893571840.....85629975876......8624298007460
.1681..1603633..141681409...10965349591...1881009507001....340129511751843
.3600..7596720.1096603225..134407778400..41320353904281..13416072442152345
.7744.36066272.8501393209.1654812479232.910635938795025.530629269304561623

Examples

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

Links

Crossrefs

Column 1 is A207170 for n>1

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6)
k=2: [order 21]
k=3: [order 45]
Empirical for row n:
n=1: a(n) = 3*a(n-1) +a(n-3) +7*a(n-4) -20*a(n-5) -2*a(n-6) -4*a(n-8) +8*a(n-9)
n=2: [order 36]

A207682 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 72, 81, 13, 19, 169, 164, 166, 169, 18, 28, 361, 336, 436, 360, 324, 25, 41, 784, 702, 964, 1030, 660, 625, 34, 60, 1681, 1488, 2132, 2310, 2032, 1292, 1156, 46, 88, 3600, 3164, 4846, 5704, 4728, 4174, 2400, 2116, 62, 129
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4....6....9....13....19.....28.....41.....60......88.....129......189
..4...16...36...81...169...361....784...1681...3600....7744...16641....35721
..6...36...72..164...336...702...1488...3164...6612...13916...29532....62032
..9...81..166..436...964..2132...4846..11301..25496...57407..131250...299913
.13..169..360.1030..2310..5704..14090..34245..81936..201951..490844..1183972
.18..324..660.2032..4728.11994..29982..77141.193184..485658.1213580..3090430
.25..625.1292.4174..9450.25076..65564.171382.433468.1150747.2968284..7722348
.34.1156.2400.8266.18940.52632.139730.379618.990368.2737864.7139792.19521802

Examples

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

Links

Crossrefs

Column 1 is A171861(n+1)
Column 2 is A207025
Column 3 is A207509
Row 1 is A000930(n+3)
Row 2 is A207170

A207762 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 82, 81, 14, 19, 169, 221, 193, 196, 21, 28, 361, 493, 663, 488, 441, 31, 41, 784, 1095, 1664, 2245, 1087, 961, 46, 60, 1681, 2654, 4018, 6552, 6459, 2305, 2116, 68, 88, 3600, 6203, 11509, 16920, 21547, 17563, 4932, 4624, 100
Offset: 1

Views

Author

R. H. Hardin Feb 19 2012

Keywords

Comments

Table starts
..2....4....6.....9.....13.....19......28.......41.......60........88
..4...16...36....81....169....361.....784.....1681.....3600......7744
..6...36...82...221....493...1095....2654.....6203....14182.....33242
..9...81..193...663...1664...4018...11509....30943....79178....213444
.14..196..488..2245...6552..16920...59252...188350...538950...1709438
.21..441.1087..6459..21547..56651..235872...862146..2629798...9529570
.31..961.2305.17563..67330.178627..887114..3733566.11979209..49800326
.46.2116.4932.48649.217902.581166.3488718.17141340.57575203.278302021

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Column 3 is A207264
Row 1 is A000930(n+3)
Row 2 is A207170

A207960 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 102, 81, 14, 19, 169, 281, 297, 196, 22, 28, 361, 699, 989, 932, 484, 35, 41, 784, 1799, 3080, 3923, 2974, 1225, 56, 60, 1681, 4706, 9994, 15839, 15921, 9723, 3136, 90, 88, 3600, 12161, 32358, 66089, 84013, 67007, 32164
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6......9......13.......19........28.........41..........60
..4...16....36.....81.....169......361.......784.......1681........3600
..6...36...102....281.....699.....1799......4706......12161.......31356
..9...81...297....989....3080.....9994.....32358.....104176......335940
.14..196...932...3923...15839....66089....274310....1137227.....4717144
.22..484..2974..15921...84013...454223...2439422...13111617....70473286
.35.1225..9723..67007..463482..3256420..22743106..159145878..1113110358
.56.3136.32164.286299.2593815.23710041.215653086.1965912435.17907299730

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Column 3 is A207495
Row 1 is A000930(n+3)
Row 2 is A207170

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

A208501 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 60, 81, 13, 26, 256, 144, 126, 169, 19, 42, 676, 324, 324, 234, 361, 28, 68, 1764, 756, 828, 650, 456, 784, 41, 110, 4624, 1728, 2124, 1794, 1406, 896, 1681, 60, 178, 12100, 3996, 5436, 4992, 4104, 3024, 1722, 3600, 88
Offset: 1

Views

Author

R. H. Hardin Feb 27 2012

Keywords

Comments

Table starts
..2....4....6...10....16....26.....42......68.....110......178......288
..4...16...36..100...256...676...1764....4624...12100....31684....82944
..6...36...60..144...324...756...1728....3996....9180....21168....48708
..9...81..126..324...828..2124...5436...13932...35676....91404...234108
.13..169..234..650..1794..4992..13806...38376..106236...295074...817362
.19..361..456.1406..4104.12654..37430..114494..341012..1037552..3103650
.28..784..896.3024..9912.33488.111328..374416.1249472..4192384.14013664
.41.1681.1722.6150.21976.79376.286754.1037300.3752320.13577396.49125954

Examples

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

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 A207590

A207305 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 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, 13, 81, 98, 64, 10, 19, 169, 271, 200, 100, 12, 28, 361, 665, 643, 350, 144, 14, 41, 784, 1675, 1759, 1271, 556, 196, 16, 60, 1681, 4344, 4939, 3773, 2239, 826, 256, 18, 88, 3600, 11081, 14446, 11497, 7093, 3641, 1168, 324, 20, 129
Offset: 1

Views

Author

R. H. Hardin Feb 16 2012

Keywords

Comments

Table starts
..2...4....6....9....13....19.....28......41......60.......88......129
..4..16...36...81...169...361....784....1681....3600.....7744....16641
..6..36...98..271...665..1675...4344...11081...28136....71908...183709
..8..64..200..643..1759..4939..14446...41505..118266...339548...975493
.10.100..350.1271..3773.11497..36868..116117..361408..1134028..3564401
.12.144..556.2239..7093.23091..79802..271023..906448..3057442.10340359
.14.196..826.3641.12169.41893.154228..558557.1985288..7118528.25615229
.16.256.1168.5581.19515.70537.274288.1050811.3937294.14887794.56536529

Examples

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

Links

Crossrefs

Column 2 is A016742
Column 3 is A207106
Column 4 is A207107
Row 1 is A000930(n+3)
Row 2 is A207170

Formula

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n
k=4: a(n) = (5/12)*n^4 + (13/2)*n^3 + (115/12)*n^2 - (17/2)*n + 1
k=5: a(n) = (8/3)*n^4 + (49/3)*n^3 + (16/3)*n^2 - (43/3)*n + 3
k=6: a(n) = (4/15)*n^5 + (45/4)*n^4 + (199/6)*n^3 - (73/4)*n^2 - (373/30)*n + 5
k=7: a(n) = (187/60)*n^5 + (153/4)*n^4 + (455/12)*n^3 - (249/4)*n^2 + (209/30)*n + 4

A207785 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 0 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 9, 13, 81, 98, 81, 13, 18, 169, 257, 253, 169, 19, 25, 324, 611, 791, 621, 361, 28, 34, 625, 1326, 2173, 2200, 1575, 784, 41, 46, 1156, 2815, 5241, 6766, 6418, 4000, 1681, 60, 62, 2116, 5718, 12567, 17763, 22322, 19041, 10057, 3600, 88, 83
Offset: 1

Views

Author

R. H. Hardin Feb 20 2012

Keywords

Comments

Table starts
..2....4.....6.....9.....13.....18......25......34.......46.......62........83
..4...16....36....81....169....324.....625....1156.....2116.....3844......6889
..6...36....98...257....611...1326....2815....5718....11362....22164.....42507
..9...81...253...791...2173...5241...12567...28101....61397...131083....272789
.13..169...621..2200...6766..17763...46199..110732...257118...582114...1274558
.19..361..1575..6418..22322..65094..185613..486006..1224264..2997835...7098270
.28..784..4000.19041..75557.246087..786907.2283773..6379507.17308075..45325727
.41.1681.10057.55101.246840.887406.3121285.9855231.29800935.87179997.244806537

Examples

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

Links

Crossrefs

Column 1 is A000930(n+3)
Column 2 is A207170
Column 3 is A203084(n-2)
Row 1 is A171861(n+1)
Row 2 is A207025
Row 3 is A202371(n-2)

A207885 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 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, 13, 81, 82, 81, 14, 19, 169, 221, 177, 196, 22, 28, 361, 493, 575, 408, 484, 35, 41, 784, 1095, 1360, 1673, 942, 1225, 56, 60, 1681, 2654, 3106, 4387, 4881, 2233, 3136, 90, 88, 3600, 6203, 8652, 10207, 14225, 14825, 5348, 8100, 145, 129
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4....6.....9.....13.....19......28.......41.......60........88.......129
..4...16...36....81....169....361.....784.....1681.....3600......7744.....16641
..6...36...82...221....493...1095....2654.....6203....14182.....33242.....77781
..9...81..177...575...1360...3106....8652....22114....53620....139806....360132
.14..196..408..1673...4387..10207...33976....97989...250976....751786...2196861
.22..484..942..4881..14225..33631..138552...452415..1213630...4316538..14467167
.35.1225.2233.14825..49586.119278..618202..2332602..6535778..28238814.110355600
.56.3136.5348.45411.175747.430317.2857532.12501427.36429646.195734448.894867543

Examples

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

Links

Crossrefs

Column 1 is A001611(n+2)
Column 2 is A207436
Column 3 is A207483
Row 1 is A000930(n+3)
Row 2 is A207170
Row 3 is A207763

A207895 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 0 and 1 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 9, 36, 36, 10, 13, 81, 84, 100, 16, 19, 169, 198, 292, 256, 26, 28, 361, 462, 870, 912, 676, 42, 41, 784, 1080, 2446, 3358, 2812, 1764, 68, 60, 1681, 2520, 6952, 11196, 12040, 8928, 4624, 110, 88, 3600, 5886, 20168, 38160, 49442, 47320, 28152
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6......9......13......19.......28........41.........60.........88
..4...16....36.....81.....169.....361......784......1681.......3600.......7744
..6...36....84....198.....462....1080.....2520......5886......13746......32100
.10..100...292....870....2446....6952....20168.....57838.....164914.....473632
.16..256...912...3358...11196...38160...135714....471374....1605156....5575548
.26..676..2812..12040...49442..205258...856480...3559040...14795830...61589756
.42.1764..8928..47320..231900.1153532..5888458..29719004..148308700..747498440
.68.4624.28152.182192.1070030.6420722.39828558.243318702.1460399404.8907998820

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207341
Column 4 is A207662
Row 1 is A000930(n+3)
Row 2 is A207170
Showing 1-10 of 17 results. Next

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