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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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A202252 T(n,k)=Number of zero-sum -k..k arrays of n elements with adjacent element differences also in -k..k.

Original entry on oeis.org

1, 1, 1, 1, 3, 3, 1, 3, 9, 7, 1, 5, 17, 31, 15, 1, 5, 27, 81, 107, 33, 1, 7, 41, 171, 397, 387, 75, 1, 7, 57, 309, 1077, 2003, 1415, 171, 1, 9, 75, 509, 2385, 6963, 10239, 5231, 391, 1, 9, 97, 779, 4643, 18841, 45523, 52697, 19477, 899, 1, 11, 121, 1133, 8211, 43293, 150523
Offset: 1

Views

Author

R. H. Hardin Dec 14 2011

Keywords

Comments

Table starts
...1.....1.......1........1........1.........1..........1..........1
...1.....3.......3........5........5.........7..........7..........9
...3.....9......17.......27.......41........57.........75.........97
...7....31......81......171......309.......509........779.......1133
..15...107.....397.....1077.....2385......4643.......8211......13533
..33...387....2003.....6963....18841.....43293......88301.....164873
..75..1415...10239....45523...150523....408211.....960501....2031401
.171..5231...52697...300417..1212443...3882871...10536609...25247111
.391.19477..273021..1995897..9832015..37183105..116366779..315903491
.899.72933.1422337.13332697.80165217.358012837.1292162535.3974268379

Examples

			Some solutions for n=6 k=7
..0...-4....6....0...-3....0....2...-7....3...-3....0....5....3....0...-2...-4
..4...-1....0....3...-5....7...-1...-1...-4...-6...-6....4....1....6...-4...-1
..4...-1...-2....0...-4....0....4...-1...-2....0....1....3...-2....3....0....1
.-3....1...-3....4....2...-1....1....4...-3....6...-1...-2...-3...-4....6....6
..1....0....0...-1....3...-3...-1....0....1....4....2...-4...-1...-2...-1....0
.-6....5...-1...-6....7...-3...-5....5....5...-1....4...-6....2...-3....1...-2

Links

Crossrefs

Column 1 is A136029

A199898 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

Original entry on oeis.org

1, 1, 3, 1, 5, 7, 1, 7, 15, 15, 1, 9, 25, 49, 33, 1, 11, 37, 111, 159, 75, 1, 13, 51, 209, 461, 533, 171, 1, 15, 67, 351, 1043, 2035, 1783, 391, 1, 17, 85, 545, 2031, 5725, 8823, 6027, 899, 1, 19, 105, 799, 3573, 13363, 30199, 39053, 20437, 2077, 1, 21, 127, 1121, 5839
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Table starts
....1.....1......1.......1........1........1.........1.........1..........1
....3.....5......7.......9.......11.......13........15........17.........19
....7....15.....25......37.......51.......67........85.......105........127
...15....49....111.....209......351......545.......799......1121.......1519
...33...159....461....1043.....2031.....3573......5839......9021......13333
...75...533...2035....5725....13363....27457.....51395.....89577.....147547
..171..1783...8823...30199....82555...193689....406575....783989....1413739
..391..6027..39053..164993...536967..1462859...3500269...7584081...15191479
..899.20437.172355..890299..3409609.10651367..28684325..68971571..151640029
.2077.69665.767425.4877477.22163661.80142549.245319361.661158741.1611184533

Examples

			Some solutions for n=7 k=6
..1....3....3....4...-3....4....4....0....3....3...-3...-6....4...-5....0....4
.-3...-4...-4...-6....5...-2...-6....6...-3...-5....0....3...-4....5...-3...-5
..0....1....2....2...-3....4....4...-5....0....4....3...-1....0...-4....5....1
.-1....0...-3....0....0...-1...-3....3....4....0....0....6....5....6....0...-1
..4....0....2....0....1....0....0...-6...-1....2...-2...-2...-6...-3...-3....5
.-6...-4...-2....3...-6...-5...-4....5....3....0....2....4....3....4....6....0
..5....4....2...-3....6....0....5...-3...-6...-4....0...-4...-2...-3...-5...-4

Links

Crossrefs

Column 1 is A136029(n+1)
Row 3 is A082111

Formula

Empirical for rows:
T(1,k) = 1
T(2,k) = 2*k + 1
T(3,k) = k^2 + 5*k + 1
T(4,k) = (4/3)*k^3 + 6*k^2 + (20/3)*k + 1
T(5,k) = (11/12)*k^4 + (49/6)*k^3 + (193/12)*k^2 + (41/6)*k + 1
T(6,k) = (11/10)*k^5 + (55/6)*k^4 + (55/2)*k^3 + (173/6)*k^2 + (37/5)*k + 1
T(7,k) = (151/180)*k^6 + (163/15)*k^5 + (377/9)*k^4 + (395/6)*k^3 + (7429/180)*k^2 + (93/10)*k + 1
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