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 1-9 of 9 results.

A241255 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 3, 2, 4, 5, 4, 7, 4, 17, 6, 10, 10, 13, 39, 8, 15, 12, 34, 47, 87, 14, 24, 22, 71, 120, 174, 212, 20, 35, 41, 135, 446, 545, 606, 488, 30, 54, 59, 356, 1202, 3404, 2570, 2111, 1134, 48, 83, 120, 734, 3822, 11700, 25190, 13328, 6647, 2644, 70, 124, 171, 1705, 11428
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Table starts
..2....3.....4.......7........10.........15.........24.........35.........54
..2....5.....4......10........12.........22.........41.........59........120
..4...17....13......34........71........135........356........734.......1705
..6...39....47.....120.......446.......1202.......3822......11428......35540
..8...87...174.....545......3404......11700......50281.....252069.....959723
.14..212...606....2570.....25190.....124372.....752717....6264519...34987493
.20..488..2111...13328....225191....1558957...13138271..205823368.1596727720
.30.1134..6647...70264...2057343...22016913..265444281.8317272277
.48.2644.21752..390840..20539926..362503120.6509404451
.70.6118.70595.2166393.204332167.6317232175

Examples

			Some solutions for n=4 k=4
..2..2..3..3....2..2..3..2....2..2..3..3....3..3..2..3....3..3..2..2
..0..0..2..1....3..1..0..3....0..0..2..1....2..1..1..2....2..1..3..1
..0..0..0..3....2..1..1..2....0..3..2..3....2..2..0..2....0..2..2..2
..0..0..0..2....2..2..3..2....3..2..1..2....0..0..0..2....2..0..0..2

Links

Crossrefs

Column 1 is A239851
Row 1 is A159288(n+1)

Formula

Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: [order 34] for n>37
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 10] for n>12
n=3: [order 52] for n>59

A241356 T(n,k) = Number of n X k 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 2, 3, 4, 3, 4, 6, 9, 3, 7, 8, 17, 19, 4, 10, 14, 23, 51, 55, 5, 15, 20, 53, 61, 128, 72, 5, 24, 30, 103, 230, 228, 248, 124, 7, 35, 48, 160, 641, 1721, 615, 624, 243, 8, 54, 70, 344, 960, 5663, 6307, 2062, 1323, 370, 9, 83, 108, 643, 3746, 11909, 32942, 35880, 6380, 2715
Offset: 1

Views

Author

R. H. Hardin, Apr 20 2014

Keywords

Comments

Table starts
..2..2...4.....6......8.......14........20.........30.........48.........70
..3..3...9....17.....23.......53.......103........160........344........643
..4..3..19....51.....61......230.......641........960.......3746.......9339
..7..4..55...128....228.....1721......5663......11909......69946.....220363
.10..5..72...248....615.....6307.....32942......81541.....704210....3476469
.15..5.124...624...2062....35880....247664.....921726...10840453...85630246
.24..7.243..1323...6380...183400...1904754...10693549..198803445.2384535274
.35..8.370..2715..17325...763750..12340892..109041097.3042023002
.54..9.695..5798..60671..4110488.104529676.1490516896
.83.12.956.11469.174659.18352240.729080777

Examples

			Some solutions for n=4, k=4
..3..2..3..3....3..2..3..3....3..2..3..3....3..2..3..3....3..2..3..3
..3..1..1..2....3..1..1..3....3..1..2..1....3..1..2..1....3..1..2..1
..2..1..0..1....2..1..0..1....2..3..0..3....2..3..3..3....2..3..0..3
..3..0..2..2....3..2..3..2....3..0..1..3....2..1..0..1....3..2..0..2

Links

Crossrefs

Column 1 is A159288(n+1).
Column 2 is A226503(n+8).
Row 1 is A239851.

Formula

Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3).
k=2: a(n) = a(n-3) +a(n-5).
k=3: [order 68] for n > 85.
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3).
n=2: [order 17] for n > 20.

A240046 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 2, 2, 4, 4, 4, 6, 9, 10, 6, 8, 20, 26, 22, 8, 14, 33, 72, 93, 50, 14, 20, 76, 174, 346, 309, 119, 20, 30, 117, 597, 1110, 1496, 1043, 276, 30, 48, 232, 1187, 5780, 7514, 8567, 3597, 637, 48, 70, 398, 3115, 17297, 55034, 61858, 46381, 12865, 1473, 70, 108, 675, 7269
Offset: 1

Views

Author

R. H. Hardin, Mar 31 2014

Keywords

Examples

			Table starts
..2....2......4.......6.........8..........14..........20..........30
..2....4......9......20........33..........76.........117.........232
..4...10.....26......72.......174.........597........1187........3115
..6...22.....93.....346......1110........5780.......17297.......57800
..8...50....309....1496......7514.......55034......236282.....1248277
.14..119...1043....8567.....61858......640643.....4593632....35084947
.20..276...3597...46381....515675.....8300260...104619164..1204711882
.30..637..12865..268672...4743056...119956268..2789729009.49892724623
.48.1473..45491.1556758..45158204..1944727891.80805084589
.70.3355.163686.9438166.453408919.34311716212
Some solutions for n=3 k=4
..2..3..2..2....3..2..2..2....2..3..3..3....2..3..2..2....2..3..3..3
..3..1..1..0....2..0..0..0....3..1..2..0....3..1..1..3....3..1..1..2
..3..1..2..3....2..0..0..0....2..1..2..0....2..1..1..2....3..2..2..2

Links

Crossrefs

Row and Column 1 are A239851

Formula

Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: [order 38] for n>40
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 18] for n>22
n=3: [order 76] for n>96

A241306 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 2, 5, 4, 6, 11, 6, 15, 6, 25, 8, 25, 37, 12, 57, 14, 40, 74, 116, 16, 129, 20, 89, 186, 330, 304, 28, 293, 30, 121, 646, 1462, 1145, 869, 38, 665, 48, 237, 1278, 5757, 6718, 4499, 2398, 66, 1509, 70, 390, 3418, 22343, 49918, 41336, 15827, 6813, 92, 3425, 108, 682
Offset: 1

Views

Author

R. H. Hardin, Apr 18 2014

Keywords

Comments

Table starts
....2...2.....4......6........8.........14..........20..........30..........48
....5...6....15.....25.......40.........89.........121.........237.........390
...11...6....37.....74......186........646........1278........3418........9113
...25..12...116....330.....1462.......5757.......22343.......79043......304799
...57..16...304...1145.....6718......49918......283985.....1666242.....9581018
..129..28...869...4499....41336.....490486.....5098814....41458261...447396605
..293..38..2398..15827...217785....3893262....70316883...978925384.16677156613
..665..66..6813..58043..1215485...37039909..1194164944.30759996872
.1509..92.18782.209838..6526016..307030328.16586413847
.3425.154.53067.757771.35833494.2801405991

Examples

			Some solutions for n=4 k=4
..3..2..3..2....3..2..3..2....3..2..3..3....3..2..3..2....3..2..2..2
..1..2..1..1....3..1..3..1....1..2..1..1....1..2..1..1....3..0..0..1
..2..0..0..1....1..2..2..3....3..2..2..2....3..2..0..2....1..0..2..1
..1..0..3..3....2..0..0..1....1..2..0..2....2..0..0..3....1..0..0..2

Links

Crossrefs

Column 1 is A239812
Row 1 is A239851

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-5)
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 14] for n>20

A240412 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

2, 2, 5, 4, 10, 11, 6, 32, 33, 25, 8, 80, 202, 139, 57, 14, 162, 846, 1526, 529, 129, 20, 493, 3035, 11670, 10749, 2105, 293, 30, 1109, 17075, 74655, 148536, 79090, 8258, 665, 48, 2656, 65790, 773196, 1765436, 2051450, 573490, 32480, 1509, 70, 7235, 283052
Offset: 1

Views

Author

R. H. Hardin, Apr 04 2014

Keywords

Comments

Table starts
....2......2.........4...........6............8............14............20
....5.....10........32..........80..........162...........493..........1109
...11.....33.......202.........846.........3035.........17075.........65790
...25....139......1526.......11670........74655........773196.......5429095
...57....529.....10749......148536......1765436......33373526.....425530595
..129...2105.....79090.....2051450.....45245148....1615637679...38249442962
..293...8258....573490....27295809...1123774316...74389514201.3275332362582
..665..32480...4185321...377924479..29595088887.3790596926634
.1509.127944..30488162..5090700587.749274246946
.3425.503372.222232658.70407569019

Examples

			Some solutions for n=4 k=4
..3..2..2..2....3..2..3..2....3..2..3..2....2..3..3..2....3..2..3..3
..3..0..0..0....1..2..1..2....1..0..3..2....2..3..2..2....2..1..1..1
..2..0..0..1....3..2..2..2....3..0..0..0....2..0..0..3....3..1..2..0
..3..0..1..2....3..1..1..2....1..2..0..2....2..0..1..2....3..0..0..0

Links

Crossrefs

Column 1 is A239812
Row 1 is A239851

Formula

Empirical for column k:
k=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)
k=2: [order 14]
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 15] for n>16

A241397 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 2, 3, 4, 5, 4, 6, 9, 13, 7, 8, 23, 29, 28, 10, 14, 44, 85, 97, 64, 15, 20, 93, 201, 480, 340, 142, 24, 30, 204, 689, 1657, 2780, 1156, 318, 35, 48, 368, 1929, 8697, 15339, 17211, 4068, 726, 54, 70, 761, 4068, 31654, 129985, 160947, 102782, 14763, 1634, 83, 108
Offset: 1

Views

Author

R. H. Hardin, Apr 20 2014

Keywords

Comments

Table starts
..2....2......4........6..........8..........14..........20.........30
..3....5......9.......23.........44..........93.........204........368
..4...13.....29.......85........201.........689........1929.......4068
..7...28.....97......480.......1657........8697.......31654......92204
.10...64....340.....2780......15339......129985......667050....2949778
.15..142...1156....17211.....160947.....2234804....18589398..134190457
.24..318...4068...102782....1622867....39781828...541660724.7518340973
.35..726..14763...645484...18627122...821631365.21331876978
.54.1634..52950..3936420..196990531.16108803423
.83.3695.190950.24633252.2356216195

Examples

			Some solutions for n=4 k=4
..3..2..3..3....3..2..2..2....2..3..3..2....2..3..3..2....2..3..3..2
..1..2..1..2....2..1..0..0....2..1..2..0....2..3..2..2....1..3..1..2
..3..2..0..0....3..1..2..0....3..0..0..2....2..0..0..3....1..2..0..2
..1..0..0..0....3..2..0..0....2..0..1..0....2..1..1..3....3..2..2..2

Links

Crossrefs

Column 1 is A159288(n+1)
Row 1 is A239851

Formula

Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: [order 38]
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 22] for n>23

A241054 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 3, 2, 4, 3, 4, 7, 2, 4, 6, 10, 10, 3, 6, 8, 15, 18, 24, 6, 8, 14, 24, 18, 60, 64, 6, 12, 20, 35, 46, 93, 163, 132, 15, 13, 30, 54, 58, 297, 280, 598, 690, 31, 20, 48, 83, 102, 507, 1423, 1392, 3411, 2142, 58, 28, 70, 124, 173, 1264, 4167, 10921, 13273, 11283, 7144, 170, 38
Offset: 1

Views

Author

R. H. Hardin, Apr 15 2014

Keywords

Comments

Table starts
..2..3...4.....7......10........15..........24..........35..........54
..2..3...2....10......18........18..........46..........58.........102
..4..4...3....24......60........93.........297.........507........1264
..6..6...6....64.....163.......280........1423........4167.......13389
..8..8...6...132.....598......1392.......10921.......72769......370453
.14.12..15...690....3411.....13273......189680.....2667280....18820225
.20.13..31..2142...11283.....89910.....1511923....30914092...376386754
.30.20..58..7144...72578...1128052....35582068..1432670661.26960360814
.48.28.170.30662..404421..13331118...776191453.62057946683
.70.38.388.95669.2220973.128026529.14877945554

Examples

			Some solutions for n=4 k=4
..3..2..3..3....3..3..2..2....3..2..3..2....3..3..2..3....3..3..2..2
..2..1..1..0....2..1..1..3....2..1..1..0....2..1..1..0....2..1..1..3
..2..0..2..0....3..3..2..2....2..1..3..0....3..3..2..2....3..3..2..3
..2..0..0..0....2..0..2..0....2..1..2..0....3..1..0..0....2..1..2..3

Links

Crossrefs

Column 1 is A239851
Row 1 is A159288(n+1)

Formula

Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: a(n) = 2*a(n-2) -a(n-4) +a(n-5) -a(n-7) +a(n-8) +a(n-11) for n>15
Empirical for row n:
n=1: a(n) = a(n-2) +2*a(n-3)
n=2: [order 15] for n>17
n=3: [order 70] for n>85

A240760 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or zero plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.

Original entry on oeis.org

2, 5, 2, 11, 6, 4, 25, 9, 12, 6, 57, 42, 19, 16, 8, 129, 124, 142, 24, 16, 14, 293, 474, 553, 348, 25, 35, 20, 665, 1440, 4112, 1750, 653, 35, 35, 30, 1509, 5239, 18373, 20657, 5325, 1809, 45, 36, 48, 3425, 16730, 131958, 149324, 77314, 21859, 3606, 76, 65, 70, 7773
Offset: 1

Views

Author

R. H. Hardin, Apr 12 2014

Keywords

Comments

Table starts
..2..5..11....25......57......129.......293........665........1509.......3425
..2..6...9....42.....124......474......1440.......5239.......16730......58945
..4.12..19...142.....553.....4112.....18373.....131958......625820....4472258
..6.16..24...348....1750....20657....149324....1954881....16557694..232884150
..8.16..25...653....5325....77314....947937...21847993...336059014.9470457699
.14.35..35..1809...21859...500139...9748926..420731038.11098085704
.20.35..45..3606...66809..2319189..75889699.5873834148
.30.36..76..8307..222091.11311246.583512422
.48.65.117.20609..811643.62333325
.70.83.180.42658.2448916

Examples

			Some solutions for n=4 k=4
..3..3..1..1....2..2..2..2....3..3..1..3....2..1..1..3....2..2..3..3
..2..0..2..3....3..3..1..1....2..0..0..2....3..3..0..2....3..1..0..2
..2..0..2..3....3..2..0..1....3..1..0..2....2..1..3..2....2..0..1..3
..2..0..0..2....2..0..2..2....3..1..0..2....2..0..1..2....2..0..1..3

Links

Crossrefs

Column 1 is A239851
Row 1 is A239812

Formula

Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: a(n) = 3*a(n-3) +a(n-5) -2*a(n-8) -4*a(n-9) -a(n-11) +2*a(n-14) for n>17
k=3: [order 76] for n>84
Empirical for row n:
n=1: a(n) = a(n-1) +2*a(n-2) +2*a(n-3)

A240327 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

2, 2, 2, 4, 5, 4, 6, 17, 17, 6, 8, 37, 116, 37, 8, 14, 80, 455, 455, 80, 14, 20, 213, 1677, 3374, 1677, 213, 20, 30, 443, 8091, 21455, 21455, 8091, 443, 30, 48, 1028, 28448, 189549, 247187, 189549, 28448, 1028, 48, 70, 2511, 117304, 1190246, 3898804
Offset: 1

Views

Author

R. H. Hardin, Apr 03 2014

Keywords

Comments

Table starts
..2....2.......4.........6............8............14............20
..2....5......17........37...........80...........213...........443
..4...17.....116.......455.........1677..........8091.........28448
..6...37.....455......3374........21455........189549.......1190246
..8...80....1677.....21455.......247187.......3898804......43979526
.14..213....8091....189549......3898804.....113751796....2343565571
.20..443...28448...1190246.....43979526....2343565571...88562956949
.30.1028..117304...8903613....602874070...58754628922.4085612680937
.48.2511..513841..70945972...8649395684.1550370290554
.70.5370.1871262.460466581.101952716878

Examples

			Some solutions for n=4 k=4
..3..2..3..2....3..2..3..3....2..3..3..2....3..2..2..2....3..2..3..2
..2..1..2..3....2..1..2..2....3..0..1..3....2..1..1..1....2..3..2..1
..3..1..3..2....3..2..2..0....3..1..1..2....3..0..2..2....3..0..0..2
..2..3..2..2....3..2..2..2....2..3..3..2....3..2..2..2....3..2..0..0

Links

Crossrefs

Column 1 is A239851

Formula

Empirical for column k:
k=1: a(n) = a(n-2) +2*a(n-3)
k=2: [order 13] for n>14
Showing 1-9 of 9 results.

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

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