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.

A221519 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 6, 10, 36, 94, 274, 768, 2182, 6170, 17476, 49470, 140066, 396544, 1122694, 3178538, 8999012, 25477790, 72132146, 204218880, 578179846, 1636929594, 4634437764, 13120914558, 37147634242, 105171535360, 297759253766
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 3 of A221524.

Examples

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

Links

Formula

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

A221520 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 12, 30, 144, 536, 2172, 8544, 33960, 134480, 533248, 2113456, 8377808, 33207936, 131632288, 521770784, 2068227136, 8198158272, 32496344448, 128810916224, 510588286464, 2023899853184, 8022453208832, 31799871553536, 126050200002816
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 4 of A221524.

Examples

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

Links

Crossrefs

Cf. A221524.

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.: 2*x^2*(6 + 3*x + 6*x^2 - 2*x^3 + 4*x^4) / (1 - 2*x - 6*x^2 - 6*x^3 - 4*x^4 - 4*x^6). - Colin Barker, Oct 18 2017

A221521 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 20, 68, 400, 1940, 9982, 50400, 256018, 1297924, 6584320, 33394958, 169387004, 859152000, 4357755890, 22103183110, 112110699524, 568642349004, 2884239836106, 14629299498936, 74202014273586, 376363810775194
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 5 of A221524.

Examples

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

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.: 2*x^2*(10 + 14*x + 22*x^2 - 4*x^3 + x^4) / (1 - 2*x - 11*x^2 - 20*x^3 - 17*x^4 + 3*x^5 - x^6). - Colin Barker, Oct 18 2017

A221522 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 30, 130, 900, 5368, 33380, 205080, 1264378, 7787228, 47975704, 295543282, 1820672982, 11216042008, 69095255496, 425653839018, 2622194869596, 16153749662332, 99513440156936, 613041859314376, 3776578532115986
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 6 of A221524.

Examples

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

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.: 2*x^2*(15 + 20*x + 45*x^2 - 11*x^3 + 33*x^4 + 9*x^5 + 3*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

A221523 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 42, 222, 1764, 12458, 90684, 654864, 4738970, 34274630, 247928860, 1793345580, 12971955294, 93830864024, 678713206224, 4909381705850, 35511361462492, 256866719859442, 1858011331955384, 13439678399558656, 97214130194552336
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 7 of A221524.

Examples

			Some solutions for n=6
..5....1....3....1....0....6....4....5....2....7....5....7....1....0....0....0
..3....4....7....6....3....3....6....2....5....3....0....5....6....4....3....4
..5....0....3....5....5....0....4....0....4....3....1....4....5....4....5....4
..6....0....1....1....0....4....7....2....2....5....6....7....3....7....7....2
..1....4....0....5....3....6....1....0....6....2....6....0....2....1....6....5
..4....6....2....7....0....0....3....6....2....5....0....7....6....5....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.: 2*x^2*(21 + 48*x + 108*x^2 + 34*x^3 + 36*x^4 + 12*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

A221525 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 6, 94, 536, 1940, 5368, 12458, 25544, 47776, 83240, 137078, 215608, 326444, 478616, 682690, 950888, 1297208, 1737544, 2289806, 2974040, 3812548, 4830008, 6053594, 7513096, 9241040, 11272808, 13646758, 16404344, 19590236, 23252440
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Row 5 of A221524.

Examples

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

Links

Crossrefs

Cf. A221524.

Formula

Empirical: a(n) = 1*n^5 - 1*n^4 - 10*n^3 + 38*n^2 - 60*n + 40 for n>2.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: 2*x^2*(3 + 29*x + 31*x^2 + 7*x^3 - 11*x^4 + 2*x^5 - x^6) / (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>8.
(End)

A221526 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 10, 274, 2172, 9982, 33380, 90684, 212812, 447962, 867012, 1569640, 2691164, 4410102, 6956452, 10620692, 15763500, 22826194, 32341892, 44947392, 61395772, 82569710, 109495524, 143357932, 185515532, 237517002, 301118020, 378298904
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Row 6 of A221524.

Examples

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

Links

Crossrefs

Cf. A221524.

Formula

Empirical: a(n) = 1*n^6 - 20*n^4 + 83*n^3 - 182*n^2 + 236*n - 148 for n>3.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: 2*x^2*(5 + 102*x + 232*x^2 + 91*x^3 - 61*x^4 + 3*x^5 - 15*x^6 + 4*x^7 - 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)

A221527 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 2 or more.

Original entry on oeis.org

0, 16, 768, 8544, 50400, 205080, 654864, 1763328, 4184064, 9005400, 17936160, 33537504, 59505888, 101012184, 165102000, 261162240, 401458944, 601751448, 881987904, 1267087200, 1787812320, 2481740184, 3394333008, 4580116224
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Row 7 of A221524.

Examples

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

Links

Crossrefs

Cf. A221524.

Formula

Empirical: a(n) = 1*n^7 + 1*n^6 - 29*n^5 + 109*n^4 - 204*n^3 + 202*n^2 - 80*n for n>2.
Conjectures from Colin Barker, Aug 06 2018: (Start)
G.f.: 8*x^2*(2 + 80*x + 356*x^2 + 332*x^3 - 97*x^4 - 22*x^5 - 28*x^6 + 8*x^7 - x^8) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>10.
(End)
Showing 1-8 of 8 results.

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