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 1-8 of 8 results.

A221510 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 2, 3, 12, 30, 89, 248, 706, 1995, 5652, 15998, 45297, 128240, 363074, 1027923, 2910236, 8239390, 23327177, 66043368, 186980482, 529374875, 1498754084, 4243238398, 12013359841, 34011950560, 96293859202, 272624979363
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Column 3 of A221515.

Examples

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

Links

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +3*a(n-3) +a(n-4).
Empirical g.f.: x^2*(2 + x + x^2) / ((1 + x)*(1 - 2*x - 2*x^2 - x^3)). - Colin Barker, Oct 18 2017

A221511 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 3, 7, 36, 130, 532, 2088, 8304, 32876, 130376, 516704, 2048264, 8118864, 32182256, 127565600, 505652480, 2004334368, 7944899296, 31492457536, 124831656000, 494815052864, 1961376994048, 7774621408896, 30817501320448, 122156223100160
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Column 4 of A221515.

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +6*a(n-2) +6*a(n-3) +4*a(n-4) +4*a(n-6).
Empirical g.f.: x^2*(3 + x + 4*x^2 - 2*x^3 + 2*x^4) / (1 - 2*x - 6*x^2 - 6*x^3 - 4*x^4 - 4*x^6). - Colin Barker, Oct 18 2017

A221512 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 4, 13, 80, 381, 1970, 9940, 50495, 255980, 1298632, 6586395, 33407907, 169448914, 859472004, 4359369001, 22111382192, 112152257687, 568853184739, 2885309153794, 14634723355722, 74229524701062, 376503348140640
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Column 5 of A221515.

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +11*a(n-2) +20*a(n-3) +17*a(n-4) -3*a(n-5) +a(n-6).
Empirical g.f.: x^2*(4 + 5*x + 10*x^2 - 2*x^3) / (1 - 2*x - 11*x^2 - 20*x^3 - 17*x^4 + 3*x^5 - x^6). - Colin Barker, Oct 18 2017

A221513 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 5, 21, 150, 884, 5513, 33860, 208756, 1285694, 7921082, 48795589, 300602292, 1851824780, 11407972817, 70277580919, 432937512858, 2667065000212, 16430167559715, 101216282472118, 623532037268338, 3841202145282104
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Column 6 of A221515.

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-1) +14*a(n-2) +29*a(n-3) +28*a(n-4) +a(n-5) +27*a(n-6) +8*a(n-7) +2*a(n-8).
Empirical g.f.: x^2*(5 + 6*x + 17*x^2 - 5*x^3 + 12*x^4 + 2*x^5 + 2*x^6) / (1 - 3*x - 14*x^2 - 29*x^3 - 28*x^4 - x^5 - 27*x^6 - 8*x^7 - 2*x^8). - Colin Barker, Oct 18 2017

A221514 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 6, 31, 252, 1765, 12872, 92934, 672526, 4864004, 35184566, 254499831, 1840896185, 13315870072, 96318591951, 696707724524, 5039542943168, 36452864937683, 263676961336509, 1907272308179486, 13796001136950442
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Column 7 of A221515.

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-1) +21*a(n-2) +58*a(n-3) +79*a(n-4) +32*a(n-5) +23*a(n-6) +4*a(n-7) +8*a(n-8).
Empirical g.f.: x^2*(6 + 13*x + 33*x^2 + 10*x^3 + 13*x^4 - 4*x^5 + 4*x^6) / (1 - 3*x - 21*x^2 - 58*x^3 - 79*x^4 - 32*x^5 - 23*x^6 - 4*x^7 - 8*x^8). - Colin Barker, Oct 18 2017

A221516 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 3, 30, 130, 381, 884, 1765, 3174, 5285, 8296, 12429, 17930, 25069, 34140, 45461, 59374, 76245, 96464, 120445, 148626, 181469, 219460, 263109, 312950, 369541, 433464, 505325, 585754, 675405, 774956, 885109, 1006590, 1140149, 1286560
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Row 5 of A221515.

Examples

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

Links

Crossrefs

Cf. A221515.

Formula

Empirical: a(n) = 1*n^4 - 1*n^3 - 10*n^2 + 33*n - 34 for n>3.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: x^2*(3 + 15*x + 10*x^2 + x^3 - 6*x^4 + 2*x^5 - x^6) / (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>8.
(End)

A221517 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 5, 89, 532, 1970, 5513, 12872, 26477, 49598, 86465, 142388, 223877, 338762, 496313, 707360, 984413, 1341782, 1795697, 2364428, 3068405, 3930338, 4975337, 6231032, 7727693, 9498350, 11578913, 14008292, 16828517, 20084858, 23825945
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Row 6 of A221515.

Examples

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

Links

Crossrefs

Cf. A221515.

Formula

Empirical: a(n) = 1*n^5 - 20*n^3 + 78*n^2 - 146*n + 125 for n>4.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: x^2*(5 + 59*x + 73*x^2 + 13*x^3 - 32*x^4 + 9*x^5 - 9*x^6 + 3*x^7 - x^8) / (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>10.
(End)

A221518 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more, starting with 0.

Original entry on oeis.org

0, 8, 248, 2088, 9940, 33860, 92934, 219352, 463208, 898020, 1626970, 2789864, 4570812, 7206628, 10995950, 16309080, 23598544, 33410372, 46396098, 63325480, 85099940, 112766724, 147533782, 190785368, 244098360, 309259300, 388282154
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2013

Keywords

Comments

Row 7 of A221515.

Examples

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

Links

Crossrefs

Cf. A221515.

Formula

Empirical: a(n) = 1*n^6 + 1*n^5 - 29*n^4 + 104*n^3 - 173*n^2 + 136*n - 40 for n>3.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: 2*x^2*(4 + 96*x + 260*x^2 + 126*x^3 - 136*x^4 + 43*x^5 - 49*x^6 + 19*x^7 - 3*x^8) / (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>10.
(End)
Showing 1-8 of 8 results.

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