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 11-19 of 19 results.

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

A208688 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

Original entry on oeis.org

2, 4, 4, 6, 16, 6, 10, 36, 36, 9, 16, 100, 78, 81, 14, 26, 256, 282, 189, 196, 21, 42, 676, 768, 927, 490, 441, 31, 68, 1764, 2430, 2889, 3430, 1113, 961, 46, 110, 4624, 7086, 11727, 12096, 11067, 2449, 2116, 68, 178, 12100, 21588, 40581, 66094, 41013, 34627
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..189....927...2889...11727....40581....154359.....554733.....2062215
.14..196..490...3430..12096...66094...269766...1331988....5795314....27403166
.21..441.1113..11067..41013..301035..1346961...8556723...42184905...249260739
.31..961.2449..34627.133207.1332721..6398617..53340739..290904031..2188890625
.46.2116.5474.111642.444912.6219706.31733422.358035204.2130519946.21086588370

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Column 3 is A207724
Row 1 is A006355(n+2)
Row 2 is A206981

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)=a(k-1)+10*a(k-2)+2*a(k-3)-10*a(k-4)
n=5: a(k)=a(k-1)+17*a(k-2)+4*a(k-3)-32*a(k-4)
n=6: a(k)=a(k-1)+26*a(k-2)+6*a(k-3)-78*a(k-4)
n=7: a(k)=a(k-1)+39*a(k-2)+9*a(k-3)-180*a(k-4)

A207391 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 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, 21, 196, 271, 200, 100, 12, 31, 441, 834, 643, 350, 144, 14, 46, 961, 2307, 2356, 1271, 556, 196, 16, 68, 2116, 6115, 7561, 5348, 2239, 826, 256, 18, 100, 4624, 16544, 23071, 19319, 10570, 3641, 1168, 324, 20, 147
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Table starts
..2...4....6....9....14.....21.....31......46.......68......100.......147
..4..16...36...81...196....441....961....2116.....4624....10000.....21609
..6..36...98..271...834...2307...6115...16544....44250...116526....307117
..8..64..200..643..2356...7561..23071...72410...223804...678174...2060069
.10.100..350.1271..5348..19319..65955..232892...806886..2731598...9282799
.12.144..556.2239.10570..42167.158217..616386..2348280..8718366..32527713
.14.196..826.3641.18972..82477.335915.1424240..5887228.23664574..95673277
.16.256.1168.5581.31710.148743.651531.2975974.13215696.56972122.247183399

Examples

			Some solutions for n=4 k=3
..1..0..0....0..0..0....0..1..1....1..1..1....1..1..1....1..0..1....1..0..1
..0..0..0....0..1..1....1..1..0....1..1..1....1..0..1....1..0..1....0..1..1
..1..0..0....0..1..1....1..1..1....1..1..1....1..1..1....1..0..1....0..1..1
..0..0..0....0..1..1....1..1..1....1..1..1....1..1..1....1..0..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 A038718(n+2)
Row 2 is A207069

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) = (2/15)*n^5 + (55/12)*n^4 + (101/6)*n^3 + (5/12)*n^2 - (299/30)*n + 2
k=6: a(n) = (1/36)*n^6 + (113/60)*n^5 + (151/9)*n^4 + (95/4)*n^3 - (605/36)*n^2 - (229/30)*n + 3
k=7: a(n) = (1/210)*n^7 + (103/180)*n^6 + (197/20)*n^5 + (1439/36)*n^4 + (293/20)*n^3 - (3469/90)*n^2 + (157/105)*n + 3

A207774 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 1 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, 84, 81, 14, 26, 256, 292, 192, 196, 21, 42, 676, 912, 828, 450, 441, 31, 68, 1764, 2812, 3130, 2514, 972, 961, 46, 110, 4624, 8928, 11230, 11950, 7164, 2040, 2116, 68, 178, 12100, 28152, 43260, 49122, 43264, 20104
Offset: 1

Views

Author

R. H. Hardin Feb 20 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...84...292....912....2812.....8928.....28152......87972......277292
..9...81..192...828...3130...11230....43260....163710.....604340.....2295512
.14..196..450..2514..11950...49122...240346...1128862....4877154....23327018
.21..441..972..7164..43264..195160..1246206...7381202...35627804...220514498
.31..961.2040.20104.157472..759482..6513576..49975640..259077468..2150453548
.46.2116.4278.57458.597090.3023026.35632160.364308938.1972417684.22562076620

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Row 1 is A006355(n+2)
Row 2 is A206981
Row 3 is A207341
Row 4 is A207342

A208164 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 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, 287, 196, 21, 28, 361, 699, 981, 882, 441, 31, 41, 784, 1799, 2920, 3893, 2491, 961, 46, 60, 1681, 4706, 9039, 14446, 13825, 6759, 2116, 68, 88, 3600, 12161, 28681, 55576, 63031, 46611, 18528
Offset: 1

Views

Author

R. H. Hardin Feb 24 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...102....281.....699....1799.....4706.....12161......31356.......81206
..9...81...287....981....2920....9039....28681.....89623.....278652......872602
.14..196...882...3893...14446...55576...222487....873641....3397748....13352522
.21..441..2491..13825...63031..297702..1474641...7151473...34264481...166182659
.31..961..6759..46611..258952.1493661..9072707..53874293..315713411..1874906825
.46.2116.18528.159545.1088966.7719181.57903614.424153857.3061342878.22414028568

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069
Column 3 is A207237
Row 1 is A000930(n+3)
Row 2 is A207170
Row 3 is A207961

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

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

A207419 T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 1 and 0 1 0 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, 14, 81, 92, 81, 14, 21, 196, 241, 241, 196, 21, 31, 441, 720, 742, 720, 441, 31, 46, 961, 1889, 2760, 2760, 1889, 961, 46, 68, 2116, 4719, 8465, 13260, 8465, 4719, 2116, 68, 100, 4624, 12102, 24317, 50139, 50139, 24317, 12102
Offset: 1

Views

Author

R. H. Hardin Feb 17 2012

Keywords

Comments

Table starts
..2....4.....6.....9.....14......21.......31........46........68........100
..4...16....36....81....196.....441......961......2116......4624......10000
..6...36....92...241....720....1889.....4719.....12102.....30414......74588
..9...81...241...742...2760....8465....24317.....73405....214117.....601411
.14..196...720..2760..13260...50139...175903....656508...2338562....7964440
.21..441..1889..8465..50139..220882...891720...3919354..16153614...62844340
.31..961..4719.24317.175903..891720..4094666..21072638..99746042..440141222
.46.2116.12102.73405.656508.3919354.21072638.129528304.721835038.3728749264

Examples

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

Links

Crossrefs

Column 1 is A038718(n+2)
Column 2 is A207069

A061583 a(1) = 1, a(n) is the number obtained by replacing each digit of a(n-1) with five times its value.

Original entry on oeis.org

1, 5, 25, 1025, 501025, 250501025, 10250250501025, 501025010250250501025, 2505010250501025010250250501025, 1025025050102502505010250501025010250250501025
Offset: 1

Views

Author

Amarnath Murthy, May 13 2001

Keywords

Comments

Number of digits of each term is the sequence A038718. - Dmitry Kamenetsky, Jan 17 2009

Links

Crossrefs

Cf. A061581, A061582, A061584, A061585, A061586, A061587.

Programs

  • Maple
    a:= proc(n) option remember; `if`(n=1, 1, (s-> parse(cat(
      seq(parse(s[i])*5, i=1..length(s)))))(""||(a(n-1))))
    end:
seq(a(n), n=1..10);  # Alois P. Heinz, May 25 2018
  • Mathematica
    NestList[FromDigits[Flatten[IntegerDigits/@(5*IntegerDigits[#])]]&,1,10] (* Harvey P. Dale, Dec 31 2013 *)
  • Python
    def A061583_first(n):
    an = "1"
    a061583 = []
    while n > 1:
        a061583.append(int(an))
        newan = ""
        for i in an:
            newan += str(5*int(i))
        an = newan
        n -= 1
    a061583.append(int(an))
    return a061583 # John Cerkan, May 25 2018

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Asher Auel, May 15 2001
Previous Showing 11-19 of 19 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.