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.

A199899 Number of -n..n arrays x(0..3) of 4 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

Original entry on oeis.org

15, 49, 111, 209, 351, 545, 799, 1121, 1519, 2001, 2575, 3249, 4031, 4929, 5951, 7105, 8399, 9841, 11439, 13201, 15135, 17249, 19551, 22049, 24751, 27665, 30799, 34161, 37759, 41601, 45695, 50049, 54671, 59569, 64751, 70225, 75999, 82081, 88479, 95201
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 4 of A199898.

Examples

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

Links

Crossrefs

Cf. A199898.

Formula

Empirical: a(n) = (4/3)*n^3 + 6*n^2 + (20/3)*n + 1.
Conjectures from Colin Barker, Feb 23 2018: (Start)
G.f.: x*(3 - x)*(5 - 2*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)

A199892 Number of -2..2 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, 5, 15, 49, 159, 533, 1783, 6027, 20437, 69665, 238191, 817083, 2809845, 9685397, 33450675, 115736335, 401065951, 1391807783, 4836111471, 16823523661, 58586196339, 204217367081, 712482836479, 2487770630935, 8693076444331
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 2 of A199898

Examples

			Some solutions for n=6
.-2....1...-1...-1...-1....1....1...-2...-1....0....2....0....1....0...-2....0
..0...-1....0....0....2...-1...-1....0....0....1....0...-2....0....2....1....1
..0....0....0...-1...-1....0....1....2....0...-1....0....0...-2...-2...-1...-1
..0....2....0....2....2....0...-2...-1....2....0...-2....2....0....1....2....1
..2...-2....2...-1....0....0....0....1...-2....1....0...-2....1...-1...-1....0
..0....0...-1....1...-2....0....1....0....1...-1....0....2....0....0....1...-1

Links

A199893 Number of -3..3 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, 7, 25, 111, 461, 2035, 8823, 39053, 172355, 767425, 3420017, 15311495, 68665323, 308805403, 1391091909, 6278869703, 28381760049, 128482271031, 582346682067, 2642616002605, 12004291295381, 54583533395613, 248409301882015
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 3 of A199898

Examples

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

Links

A199894 Number of -4..4 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, 9, 37, 209, 1043, 5725, 30199, 164993, 890299, 4877477, 26632013, 146499083, 805700567, 4449304857, 24590147861, 136249639279, 755738351775, 4199211521573, 23357174342185, 130088542750275, 725223072283995
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 4 of A199898

Examples

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

Links

A199895 Number of -5..5 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, 11, 51, 351, 2031, 13363, 82555, 536967, 3409609, 22163661, 142744843, 930121865, 6040974735, 39482258363, 257848379869, 1690142722447, 11081263427471, 72823380368573, 478876538926483, 3154101346620987
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 5 of A199898

Examples

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

Links

A199896 Number of -6..6 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, 13, 67, 545, 3573, 27457, 193689, 1462859, 10651367, 80142549, 593254327, 4466635929, 33386730231, 251884546233, 1894568061637, 14327147198653, 108231414777793, 820328179730055, 6216861991058925, 47216885967426099
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 6 of A199898

Examples

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

Links

A199897 Number of -7..7 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, 15, 85, 799, 5839, 51395, 406575, 3500269, 28684325, 245319361, 2048301005, 17499467353, 147731409251, 1263413909311, 10741266363733, 92019265611439, 786112365529335, 6747253002120179, 57843127733658007, 497375672047480891
Offset: 1

Views

Author

R. H. Hardin Nov 11 2011

Keywords

Comments

Column 7 of A199898

Examples

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

Links

A199900 Number of -n..n arrays x(0..4) of 5 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

Original entry on oeis.org

33, 159, 461, 1043, 2031, 3573, 5839, 9021, 13333, 19011, 26313, 35519, 46931, 60873, 77691, 97753, 121449, 149191, 181413, 218571, 261143, 309629, 364551, 426453, 495901, 573483, 659809, 755511, 861243, 977681, 1105523, 1245489, 1398321
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 5 of A199898.

Examples

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

Links

Crossrefs

Cf. A199898.

Formula

Empirical: a(n) = (11/12)*n^4 + (49/6)*n^3 + (193/12)*n^2 + (41/6)*n + 1.
Conjectures from Colin Barker, May 16 2018: (Start)
G.f.: x*(33 - 6*x - 4*x^2 - 2*x^3 + x^4) / (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)

A199901 Number of -n..n arrays x(0..5) of 6 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

Original entry on oeis.org

75, 533, 2035, 5725, 13363, 27457, 51395, 89577, 147547, 232125, 351539, 515557, 735619, 1024969, 1398787, 1874321, 2471019, 3210661, 4117491, 5218349, 6542803, 8123281, 9995203, 12197113, 14770811, 17761485, 21217843, 25192245, 29740835
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 6 of A199898.

Examples

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

Links

Crossrefs

Cf. A199898.

Formula

Empirical: a(n) = (11/10)*n^5 + (55/6)*n^4 + (55/2)*n^3 + (173/6)*n^2 + (37/5)*n + 1.
Conjectures from Colin Barker, May 16 2018: (Start)
G.f.: x*(75 + 83*x - 38*x^2 + 10*x^3 + 3*x^4 - x^5) / (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)

A199902 Number of -n..n arrays x(0..6) of 7 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.

Original entry on oeis.org

171, 1783, 8823, 30199, 82555, 193689, 406575, 783989, 1413739, 2414499, 3942247, 6197307, 9431995, 13958869, 20159583, 28494345, 39511979, 53860591, 72298839, 95707807, 125103483, 161649841, 206672527, 261673149, 328344171, 408584411
Offset: 1

Views

Author

R. H. Hardin, Nov 11 2011

Keywords

Comments

Row 7 of A199898.

Examples

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

Links

Crossrefs

Cf. A199898.

Formula

Empirical: a(n) = (151/180)*n^6 + (163/15)*n^5 + (377/9)*n^4 + (395/6)*n^3 + (7429/180)*n^2 + (93/10)*n + 1.
Conjectures from Colin Barker, May 17 2018: (Start)
G.f.: x*(171 + 586*x - 67*x^2 - 104*x^3 + 25*x^4 - 8*x^5 + x^6) / (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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