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 1-10 of 10 results.

A199524 Number of -2..2 arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

1, 4, 18, 72, 320, 1414, 6346, 28766, 131246, 602390, 2777638, 12857572, 59712940, 278096674, 1298309782, 6074112952, 28470828008, 133671581490, 628526085270, 2959291856816, 13950087683416, 65832860408434, 310987879638926
Offset: 1

Views

Author

R. H. Hardin Nov 07 2011

Keywords

Comments

Column 2 of A199530

Examples

			Some solutions for n=5
.-1....2....0...-1...-1....1...-2....2....1....1....0....0...-2....0...-1...-1
..0....1...-2....2....2....1....2...-2....0....2...-1....1....1....1....0...-2
.-2...-2....1....2....2....1...-2....2....1...-1...-1....1....2...-2....2....0
..1...-1....0...-2...-1...-2....2....0...-2....0....0...-1....1....2....1....2
..2....0....1...-1...-2...-1....0...-2....0...-2....2...-1...-2...-1...-2....1

Links

A199525 Number of -3..3 arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

1, 6, 36, 212, 1324, 8342, 53302, 343710, 2232322, 14582218, 95702528, 630544704, 4168091856, 27630031358, 183604587444, 1222672695812, 8157398577024, 54515075729370, 364861668341252, 2445239266293460, 16407415704050100
Offset: 1

Views

Author

R. H. Hardin Nov 07 2011

Keywords

Comments

Column 3 of A199530

Examples

			Some solutions for n=5
..3...-2...-3...-1....0....1....3...-2....1....3...-2....0....1....2...-3....3
.-3....1....2....1....2....3....0....0...-3....3....0...-3...-3....1...-1...-2
..2....1...-3....0...-2...-1....1....2....0...-3...-1....1....2...-2....3....1
.-3....3....3....1...-2...-1...-3...-2...-1....0....3....2....1...-3...-2...-2
..1...-3....1...-1....2...-2...-1....2....3...-3....0....0...-1....2....3....0

Links

A199526 Number of -4..4 arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

1, 8, 60, 464, 3734, 30484, 252154, 2105064, 17701326, 149708146, 1272108368, 10851700690, 92875809416, 797134845184, 6858361265978, 59133629878796, 510815878314050, 4419961056157870, 38301854208088068, 332355738077962284
Offset: 1

Views

Author

R. H. Hardin, Nov 07 2011

Keywords

Comments

Column 4 of A199530.

Examples

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

Links

Crossrefs

Cf. A199530.

A199527 Number of -5..5 arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

1, 10, 90, 860, 8470, 84852, 860854, 8815392, 90927530, 943302430, 9832131238, 102882332054, 1080105471952, 11371474312404, 120012768975248, 1269300095287288, 13449845528174042, 142756162602411602
Offset: 1

Views

Author

R. H. Hardin Nov 07 2011

Keywords

Comments

Column 5 of A199530

Examples

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

Links

A199528 Number of -6..6 arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

1, 12, 126, 1432, 16682, 197962, 2378412, 28844590, 352355640, 4329146404, 53439881140, 662256127274, 8234161234932, 102668802658902, 1283270183281782, 16074009129375488, 201718956009659774, 2535677513896048744
Offset: 1

Views

Author

R. H. Hardin Nov 07 2011

Keywords

Comments

Column 6 of A199530

Examples

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

Links

A199529 Number of -7..7 arrays x(0..n-1) of n elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

1, 14, 168, 2212, 29750, 407946, 5662636, 79345982, 1119873360, 15897133212, 226731289148, 3246399497138, 46636478912912, 671855095655758, 9702557118121642, 140418234266554336, 2035998107250999870
Offset: 1

Views

Author

R. H. Hardin Nov 07 2011

Keywords

Comments

Column 7 of A199530

Examples

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

Links

A199531 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

12, 72, 212, 464, 860, 1432, 2212, 3232, 4524, 6120, 8052, 10352, 13052, 16184, 19780, 23872, 28492, 33672, 39444, 45840, 52892, 60632, 69092, 78304, 88300, 99112, 110772, 123312, 136764, 151160, 166532, 182912, 200332, 218824, 238420, 259152
Offset: 1

Views

Author

R. H. Hardin, Nov 07 2011

Keywords

Comments

Row 4 of A199530.

Examples

			Some solutions for n=5:
.-4...-4....4....0...-5....5....2....0...-1...-3....2....1....4...-1....4...-1
..4....5...-4....2....3...-2...-2...-2....0...-2...-2...-3...-1....2...-2....5
..3....1...-2...-5...-3...-1....1....1...-2....2....3....1....0....4....1....1
.-3...-2....2....3....5...-2...-1....1....3....3...-3....1...-3...-5...-3...-5

Links

Crossrefs

Cf. A199530.

Formula

Empirical: a(n) = (16/3)*n^3 + 8*n^2 - (4/3)*n.
Conjectures from Colin Barker, May 15 2018: (Start)
G.f.: 4*x*(3 + 6*x - x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A199532 Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

32, 320, 1324, 3734, 8470, 16682, 29750, 49284, 77124, 115340, 166232, 232330, 316394, 421414, 550610, 707432, 895560, 1118904, 1381604, 1688030, 2042782, 2450690, 2916814, 3446444, 4045100, 4718532, 5472720, 6313874, 7248434, 8283070
Offset: 1

Views

Author

R. H. Hardin, Nov 07 2011

Keywords

Comments

Row 5 of A199530.

Examples

			Some solutions for n=5:
..2....1....3...-5....1....0....5....5...-3....4...-5....1...-5...-2....0...-1
.-5...-2....4....4....4...-1...-3....0...-1...-3....1....0....3....3....1....5
.-4...-2...-4....1....3....1...-3...-2....2...-5....2...-5...-2...-3...-3....3
..3....4...-1...-2...-5....3...-1...-1...-3...-1....2....4...-1...-2...-3...-3
..4...-1...-2....2...-3...-3....2...-2....5....5....0....0....5....4....5...-4

Links

Crossrefs

Cf. A199530.

Formula

Empirical: a(n) = (115/12)*n^4 + (115/6)*n^3 + (41/12)*n^2 - (1/6)*n.
Conjectures from Colin Barker, May 15 2018: (Start)
G.f.: 2*x*(16 + 80*x + 22*x^2 - 3*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A199533 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

80, 1414, 8342, 30484, 84852, 197962, 407946, 766664, 1341816, 2219054, 3504094, 5324828, 7833436, 11208498, 15657106, 21416976, 28758560, 37987158, 49445030, 63513508, 80615108, 101215642, 125826330, 155005912, 189362760, 229556990
Offset: 1

Views

Author

R. H. Hardin, Nov 07 2011

Keywords

Comments

Row 6 of A199530.

Examples

			Some solutions for n=5:
..1....5...-4....0....5...-3...-1...-3....5....5...-5....0...-3....3....3....4
..3....1....2....5....5...-1....2...-4....4...-3...-2...-3....4....3....1...-1
..3...-5...-3...-3....1...-1....5....1...-5....3....3....4...-3...-1....3....1
.-1....0....4...-2...-3...-4...-3...-2....0....0....5....0...-1...-5....0....0
.-2...-3....4...-4...-3....4...-2....3...-5...-5....2...-3...-1....2...-2...-2
.-4....2...-3....4...-5....5...-1....5....1....0...-3....2....4...-2...-5...-2

Links

Crossrefs

Cf. A199530.

Formula

Empirical: a(n) = (88/5)*n^5 + 44*n^4 + (58/3)*n^3 - 3*n^2 + (31/15)*n.
Conjectures from Colin Barker, May 15 2018: (Start)
G.f.: 2*x*(40 + 467*x + 529*x^2 + 21*x^3 - x^4) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A199534 Number of -n..n arrays x(0..6) of 7 elements with zero sum and no two consecutive zero elements.

Original entry on oeis.org

200, 6346, 53302, 252154, 860854, 2378412, 5662636, 12071420, 23627580, 43207238, 74751754, 123503206, 196263418, 301676536, 450535152, 656109976, 934503056, 1305024546, 1790593022, 2418159346, 3219154078, 4229958436, 5492398804
Offset: 1

Views

Author

R. H. Hardin, Nov 07 2011

Keywords

Comments

Row 7 of A199530.

Examples

			Some solutions for n=5:
.-5...-5...-4...-5...-4...-5...-4...-5...-4...-5...-5...-5...-5...-4...-5...-4
..1...-3....1....3....0...-5...-4....4...-4....5...-3....0....5...-4....3....2
..1....4...-1....0....4....2....0...-5...-1....1...-1...-2....3....1...-5....2
.-1...-2....3...-1....5...-2....5....5...-2....3...-1....4...-3....4....1....0
..4...-4...-4....1...-2....5...-1....2....3...-3....5....1....0....4....5...-1
..5....5....3...-2...-1....5...-1....0....3...-5....0....4...-2....1....5....1
.-5....5....2....4...-2....0....5...-1....5....4....5...-2....2...-2...-4....0

Links

Crossrefs

Cf. A199530.

Formula

Empirical: a(n) = (5887/180)*n^6 + (5887/60)*n^5 + (620/9)*n^4 + (11/12)*n^3 + (433/180)*n^2 - (91/30)*n.
Conjectures from Colin Barker, May 16 2018: (Start)
G.f.: 2*x*(100 + 2473*x + 6540*x^2 + 2653*x^3 + 4*x^4 + 4*x^5) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
Showing 1-10 of 10 results.

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