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.

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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

A208369 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 0 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 114, 81, 14, 26, 256, 450, 351, 196, 21, 42, 676, 1644, 1953, 1162, 441, 31, 68, 1764, 6186, 9999, 9338, 3633, 961, 46, 110, 4624, 23010, 52821, 67396, 41433, 11067, 2116, 68, 178, 12100, 85992, 275769, 507682, 422541
Offset: 1

Views

Author

R. H. Hardin Feb 25 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...114....450.....1644......6186......23010........85992........320742
..9...81...351...1953.....9999.....52821.....275769......1446381.......7572429
.14..196..1162...9338....67396....507682....3759574.....28035840.....208473118
.21..441..3633..41433...422541...4503765...47178453....497691495....5235328875
.31..961.11067.177909..2563359..38542393..570085195...8487780687..126039261499
.46.2116.33994.774134.15730896.334331082.6982331490.146860432968.3080068967794

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Column 3 is A207421
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A207718

A208379 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 8, 16, 100, 72, 64, 10, 26, 256, 240, 108, 100, 12, 42, 676, 704, 420, 144, 144, 14, 68, 1764, 2080, 1344, 640, 180, 196, 16, 110, 4624, 6216, 4212, 2176, 900, 216, 256, 18, 178, 12100, 18496, 13860, 7072, 3200, 1200, 252, 324, 20, 288
Offset: 1

Views

Author

R. H. Hardin Feb 25 2012

Keywords

Comments

Table starts
..2...4...6...10...16....26....42.....68.....110.....178......288......466
..4..16..36..100..256...676..1764...4624...12100...31684....82944...217156
..6..36..72..240..704..2080..6216..18496...55000..163760...487296..1450192
..8..64.108..420.1344..4212.13860..44880..144540..468852..1517184..4906980
.10.100.144..640.2176..7072.25200..87040..296560.1028128..3545856.12198016
.12.144.180..900.3200.10660.40740.148240..526900.1931300..7015680.25336420
.14.196.216.1200.4416.14976.60984.231744..851400.3276624.12438144.46737936
.16.256.252.1540.5824.20020.86436.340816.1285900.5170900.20393856.79220932

Examples

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

Links

Crossrefs

Column 1 is A004275(n+1)
Column 2 is A016742
Column 3 is A044102(n-1) for n>1
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A207840

Formula

Empirical for column k:
k=1: a(n) = 2*n
k=2: a(n) = 4*n^2
k=3: a(n) = 36*n - 36 for n>1
k=4: a(n) = 20*n^2 + 40*n - 60 for n>1
k=5: a(n) = 96*n^2 - 32*n - 64 for n>1
k=6: a(n) = 364*n^2 - 416*n + 52 for n>1
k=7: a(n) = 84*n^3 + 840*n^2 - 1344*n + 420 for n>1
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)=a(k-1)+4*a(k-2)+5*a(k-3)+2*a(k-4)-a(k-5)+a(k-6) for k>8
n=4: a(k)=a(k-1)+4*a(k-2)+9*a(k-3)+5*a(k-4)-2*a(k-5)+4*a(k-6) for k>8
n=5: a(k)=a(k-1)+4*a(k-2)+13*a(k-3)+8*a(k-4)-3*a(k-5)+9*a(k-6) for k>8
n=6: a(k)=a(k-1)+4*a(k-2)+17*a(k-3)+11*a(k-4)-4*a(k-5)+16*a(k-6) for k>8
n=7: a(k)=a(k-1)+4*a(k-2)+21*a(k-3)+14*a(k-4)-5*a(k-5)+25*a(k-6) for k>8

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

A208555 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 90, 81, 12, 26, 256, 330, 225, 144, 16, 42, 676, 1008, 1089, 420, 256, 20, 68, 1764, 3354, 3969, 2508, 784, 400, 25, 110, 4624, 10710, 16641, 10080, 5776, 1260, 625, 30, 178, 12100, 34884, 65025, 50052, 25600, 11020
Offset: 1

Views

Author

R. H. Hardin Feb 28 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...90...330...1008...3354...10710....34884....112530.....364722
..9..81..225..1089...3969..16641...65025...263169...1046529....4198401
.12.144..420..2508..10080..50052..221340..1042416...4742628...21989868
.16.256..784..5776..25600.150544..753424..4129024..21492496..115175824
.20.400.1260.11020..52000.351140.1913940.11836400..67894220..407225740
.25.625.2025.21025.105625.819025.4862025.33930625.214476025.1439823025

Examples

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

Links

Crossrefs

Column 1 is A002620(n+2)
Column 2 is A030179(n+2)
Column 3 is A207363
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A207454

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)

A207519 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 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, 21, 196, 271, 358, 256, 26, 31, 441, 834, 1307, 1152, 676, 42, 46, 961, 2307, 5458, 5369, 3910, 1764, 68, 68, 2116, 6115, 19909, 29622, 23645, 12994, 4624, 110, 100, 4624, 16544, 68807, 137719, 174224
Offset: 1

Views

Author

R. H. Hardin Feb 18 2012

Keywords

Comments

Table starts
..2....4.....6......9......14.......21........31.........46..........68
..4...16....36.....81.....196......441.......961.......2116........4624
..6...36....98....271.....834.....2307......6115......16544.......44250
.10..100...358...1307....5458....19909.....68807.....243954......851870
.16..256..1152...5369...29622...137719....600283....2713480....12034046
.26..676..3910..23645..174224..1048423...5849409...34086388...194127326
.42.1764.12994.101233..991184..7666319..54373655..406281454..2956097240
.68.4624.43596.439063.5723716.57113109.516879019.4964342828.46263548214

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207462
Column 4 is A207463
Row 1 is A038718(n+2)
Row 2 is A207069
Row 3 is A207392

A207949 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 1 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, 12, 81, 102, 100, 16, 16, 144, 289, 370, 256, 26, 20, 256, 612, 1369, 1232, 676, 42, 25, 400, 1296, 3478, 5929, 4238, 1764, 68, 30, 625, 2340, 8836, 18172, 26569, 14406, 4624, 110, 36, 900, 4225, 18330, 55696, 98126, 117649
Offset: 1

Views

Author

R. H. Hardin Feb 21 2012

Keywords

Comments

Table starts
..2....4.....6......9......12.......16.......20........25........30.........36
..4...16....36.....81.....144......256......400.......625.......900.......1296
..6...36...102....289.....612.....1296.....2340......4225......6890......11236
.10..100...370...1369....3478.....8836....18330.....38025.....69420.....126736
.16..256..1232...5929...18172....55696...133812....321489....662256....1364224
.26..676..4238..26569...98126...362404..1007146...2798929...6501278...15100996
.42.1764.14406.117649..524104..2334784..7513176..24176889..63380130..166152100
.68.4624.49164.522729.2806686.15069924.56114310.208947025.617864520.1827049536

Examples

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

Links

Crossrefs

Column 1 is A006355(n+2)
Column 2 is A206981
Column 3 is A207249
Column 4 is A207854
Row 1 is A002620(n+2)
Row 2 is A030179(n+2)
Row 3 is A207118

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

A217982 T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..1 nXk array.

Original entry on oeis.org

2, 2, 2, 4, 2, 4, 6, 4, 4, 6, 10, 6, 16, 6, 10, 16, 10, 36, 36, 10, 16, 26, 16, 100, 98, 100, 16, 26, 42, 26, 256, 362, 362, 256, 26, 42, 68, 42, 676, 1180, 1942, 1180, 676, 42, 68, 110, 68, 1764, 4046, 8872, 8872, 4046, 1764, 68, 110, 178, 110, 4624, 13594, 43258, 54504
Offset: 1

Views

Author

R. H. Hardin Oct 16 2012

Keywords

Comments

Table starts
...2...2.....4.......6........10.........16...........26............42
...2...2.....4.......6........10.........16...........26............42
...4...4....16......36.......100........256..........676..........1764
...6...6....36......98.......362.......1180.........4046.........13594
..10..10...100.....362......1942.......8872........43258........205446
..16..16...256....1180......8872......54504.......363728.......2347480
..26..26...676....4046.....43258.....363728......3375350......30097566
..42..42..1764...13594....205446....2347480.....30097566.....368335390
..68..68..4624...46052....986288...15361400....272859916....4595712084
.110.110.12100..155494...4714274...99957900...2457033362...56890420330
.178.178.31684..525730..22573862..651962620..22187715406..706581935362
.288.288.82944.1776548.108013892.4248252712.200128757472.8763874097740

Examples

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

Links

Crossrefs

Columns 1 and 2 are A006355(n+1)
Column 3 is A206981(n-1)
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