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 1-3 of 3 results.

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

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)
Showing 1-3 of 3 results.

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