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 12 results. Next

A199697 Number of -1..1 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

Original entry on oeis.org

1, 2, 6, 8, 14, 32, 56, 100, 204, 388, 722, 1416, 2750, 5256, 10222, 19944, 38650, 75272, 147142, 287120, 561018, 1098752, 2152092, 4217620, 8276376, 16250292, 31921374, 62754072, 123440514, 242921784, 478310952, 942260548, 1856994908, 3661288036
Offset: 1

Views

Author

R. H. Hardin, Nov 09 2011

Keywords

Comments

Column 1 of A199704

Examples

			All solutions for n=5
..0...-1....1...-1....1...-1...-1....0....1...-1....0....1....1....0
.-1....1...-1....1....0....1....0...-1...-1....1....1...-1...-1....1
..1....0....0...-1...-1...-1....1....0....1....0....0....1....0...-1
.-1...-1....1....1....1....0...-1....1....0....1...-1...-1...-1....1
..1....1...-1....0...-1....1....1....0...-1...-1....0....0....1...-1

Links

Programs

  • Mathematica
    Rest@ CoefficientList[Series[((x + 1)^2*Sqrt[(1 - x)/(1 - x - 4*x^3)] - 2 x - 1)/x, {x, 0, 34}], x] (* Michael De Vlieger, Mar 08 2017 *)

Formula

G.f.: ((x+1)^2*sqrt((1-x)/(1-x-4*x^3))-2*x-1)/x. - Stefan Hollos, Mar 08 2017

A199708 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no two neighbors equal.

Original entry on oeis.org

32, 708, 4964, 20116, 59992, 147072, 314532, 608420, 1089752, 1836600, 2946204, 4537152, 6751384, 9756388, 13747296, 18948952, 25618064, 34045344, 44557532, 57519592, 73336788, 92456792, 115371796, 142620672, 174790996, 212521224
Offset: 1

Views

Author

R. H. Hardin Nov 09 2011

Keywords

Comments

Row 6 of A199704

Examples

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

Links

Formula

Empirical: a(n)=3*a(n-1)-2*a(n-2)-a(n-3)+2*a(n-5)-a(n-6)-a(n-7)+2*a(n-8)-a(n-10)-2*a(n-11)+3*a(n-12)-a(n-13)

A199698 Number of -2..2 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

Original entry on oeis.org

1, 4, 14, 52, 200, 708, 2642, 10000, 37984, 144876, 554120, 2128672, 8204180, 31697564, 122734614, 476170124, 1850664202, 7204005752, 28081918548, 109604285492, 428278469018, 1675246478864, 6559126501510, 25703606447364
Offset: 1

Views

Author

R. H. Hardin Nov 09 2011

Keywords

Comments

Column 2 of A199704

Examples

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

Links

A199699 Number of -3..3 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

Original entry on oeis.org

1, 6, 32, 168, 892, 4964, 27854, 156920, 891684, 5095360, 29236016, 168361392, 972601784, 5633548460, 32706291872, 190266981972, 1108856802378, 6472638961608, 37836350087956, 221461180199752, 1297757839607606
Offset: 1

Views

Author

R. H. Hardin Nov 09 2011

Keywords

Comments

Column 3 of A199704

Examples

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

Links

A199700 Number of -4..4 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

Original entry on oeis.org

1, 8, 52, 380, 2734, 20116, 149942, 1128388, 8545180, 65055556, 497505902, 3818857188, 29405977172, 227044808964, 1757143904470, 13626887453432, 105870556547144, 823864569255344, 6420445347122416, 50100342760566184
Offset: 1

Views

Author

R. H. Hardin Nov 09 2011

Keywords

Comments

Column 4 of A199704

Examples

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

Links

A199701 Number of -5..5 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

Original entry on oeis.org

1, 10, 82, 724, 6504, 59992, 559028, 5252900, 49700882, 472873888, 4519281222, 43353372676, 417214414596, 4026070558436, 38943205468034, 377469980604452, 3665456335373858, 35651726951195532, 347268836196275908
Offset: 1

Views

Author

R. H. Hardin Nov 09 2011

Keywords

Comments

Column 5 of A199704

Examples

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

Links

A199702 Number of -6..6 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

Original entry on oeis.org

1, 12, 114, 1236, 13324, 147072, 1643204, 18527516, 210316392, 2400684208, 27527644696, 316844861020, 3658598730648, 42361908912360, 491666143730354, 5718341649577364, 66629811252553344, 777637357808739752
Offset: 1

Views

Author

R. H. Hardin Nov 09 2011

Keywords

Comments

Column 6 of A199704

Examples

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

Links

A199703 Number of -7..7 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

Original entry on oeis.org

1, 14, 156, 1940, 24394, 314532, 4099204, 53901956, 713719390, 9503449352, 127119684220, 1706849222504, 22991898594206, 310564824249656, 4205016717658718, 57054704774633892, 775562100878527252
Offset: 1

Views

Author

R. H. Hardin Nov 09 2011

Keywords

Comments

Column 7 of A199704

Examples

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

Links

A199705 Number of -n..n arrays x(0..2) of 3 elements with zero sum and no two neighbors equal.

Original entry on oeis.org

6, 14, 32, 52, 82, 114, 156, 200, 254, 310, 376, 444, 522, 602, 692, 784, 886, 990, 1104, 1220, 1346, 1474, 1612, 1752, 1902, 2054, 2216, 2380, 2554, 2730, 2916, 3104, 3302, 3502, 3712, 3924, 4146, 4370, 4604, 4840, 5086, 5334, 5592, 5852, 6122, 6394, 6676
Offset: 1

Views

Author

R. H. Hardin, Nov 09 2011

Keywords

Comments

Row 3 of A199704.

Examples

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

Links

Crossrefs

Cf. A199704.

Formula

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

A199706 Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two neighbors equal.

Original entry on oeis.org

8, 52, 168, 380, 724, 1236, 1940, 2872, 4068, 5552, 7360, 9528, 12080, 15052, 18480, 22388, 26812, 31788, 37340, 43504, 50316, 57800, 65992, 74928, 84632, 95140, 106488, 118700, 131812, 145860, 160868, 176872, 193908, 212000, 231184, 251496
Offset: 1

Views

Author

R. H. Hardin, Nov 09 2011

Keywords

Comments

Row 4 of A199704.

Examples

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

Links

Crossrefs

Cf. A199704.

Formula

Empirical: a(n) = 3*a(n-1)-3*a(n-2)+2*a(n-3)-3*a(n-4)+3*a(n-5)-a(n-6).
Empirical g.f.: 4*x*(2 + 7*x + 9*x^2 + 4*x^3 + 2*x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, May 16 2018
Showing 1-10 of 12 results. Next

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