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.

A221591 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

0, 7, 17, 49, 139, 393, 1113, 3151, 8921, 25257, 71507, 202449, 573169, 1622743, 4594273, 13007201, 36825691, 104260057, 295178697, 835703199, 2366023849, 6698632793, 18965016483, 53693322401, 152015310561, 430382282407, 1218488508337, 3449756892049
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Column 2 of A221596.

Examples

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

Links

Programs

  • PARI
    concat(0, Vec(x^2*(7 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3) + O(x^30))) \\ Colin Barker, Jan 31 2017

Formula

a(n) = 2*a(n-1) +2*a(n-2) +a(n-3) for n>4.
G.f.: x^2*(7 + 3*x + x^2) / (1 - 2*x - 2*x^2 - x^3). - Colin Barker, Jan 31 2017

A221592 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

0, 13, 35, 169, 651, 2715, 11011, 45099, 184063, 752155, 3072247, 12550859, 51270383, 209444163, 855592375, 3495156539, 14277953839, 58326437619, 238267540647, 973339457803, 3976159254687, 16242886662499, 66353319815959, 271057918757755, 1107290419059023
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Column 4 of A221596.

Examples

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

Links

Programs

  • PARI
    concat(0, Vec(x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6) + O(x^30))) \\ Colin Barker, Jan 31 2017

Formula

a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6).
G.f.: x^2*(13 - 4*x + 12*x^2 + 4*x^3 + 8*x^4) / (1 - 3*x - 4*x^2 - 6*x^4 - 4*x^5 - 4*x^6). - Colin Barker, Jan 31 2017

A221593 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

0, 16, 44, 256, 1068, 5082, 22912, 105586, 482204, 2210256, 10115926, 46327024, 212107056, 971225210, 4446995942, 20362020404, 93233503292, 426898240022, 1954682503544, 8950108307086, 40980784959354, 187642965834692
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Column 5 of A221596.

Examples

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

Links

Formula

Empirical: a(n) = 4*a(n-1) +3*a(n-2) -6*a(n-3) +19*a(n-4) +5*a(n-5) +a(n-6).
Empirical g.f.: 2*x^2*(8 - 10*x + 16*x^2 + 4*x^3 + x^4) / (1 - 4*x - 3*x^2 + 6*x^3 - 19*x^4 - 5*x^5 - x^6). - Colin Barker, Oct 19 2017

A221594 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

0, 19, 53, 361, 1593, 8475, 41401, 210101, 1047967, 5267759, 26387005, 132384353, 663707187, 3328545333, 16690533369, 83697779149, 419705882541, 2104659535459, 10553975797069, 52923856787737, 265391103246031, 1330826582140067
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Column 6 of A221596.

Examples

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

Links

Formula

Empirical: a(n) = 4*a(n-1) +5*a(n-2) -7*a(n-3) +33*a(n-4) +17*a(n-5) +24*a(n-6) -5*a(n-7) +2*a(n-8).
Empirical g.f.: x^2*(19 - 23*x + 54*x^2 + 17*x^3 + 42*x^4 - 9*x^5 + 3*x^6) / (1 - 4*x - 5*x^2 + 7*x^3 - 33*x^4 - 17*x^5 - 24*x^6 + 5*x^7 - 2*x^8). - Colin Barker, Oct 19 2017

A221595 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

0, 22, 62, 484, 2226, 13056, 67936, 374342, 2006006, 10894988, 58789204, 318224626, 1719926984, 9302621856, 50297494954, 271995651900, 1470758893578, 7953136851900, 43005796059376, 232551746953140, 1257506529312924
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Column 7 of A221596.

Examples

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

Links

Formula

Empirical: a(n) = 5*a(n-1) +3*a(n-2) -16*a(n-3) +65*a(n-4) -14*a(n-5) +23*a(n-6) +2*a(n-7) +8*a(n-8).
Empirical g.f.: 2*x^2*(11 - 24*x + 54*x^2 - 14*x^3 + 18*x^4 + 6*x^6) / (1 - 5*x - 3*x^2 + 16*x^3 - 65*x^4 + 14*x^5 - 23*x^6 - 2*x^7 - 8*x^8). - Colin Barker, Oct 19 2017

A221597 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

32, 139, 342, 651, 1068, 1593, 2226, 2967, 3816, 4773, 5838, 7011, 8292, 9681, 11178, 12783, 14496, 16317, 18246, 20283, 22428, 24681, 27042, 29511, 32088, 34773, 37566, 40467, 43476, 46593, 49818, 53151, 56592, 60141, 63798, 67563, 71436, 75417, 79506
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Row 5 of A221596.

Examples

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

Links

Crossrefs

Cf. A221596.

Formula

Empirical: a(n) = 54*n^2 - 69*n + 63 for n>2.
Conjectures from Colin Barker, Aug 09 2018: (Start)
G.f.: x*(32 + 43*x + 21*x^2 + 10*x^3 + 2*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
(End)

A221598 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

64, 393, 1210, 2715, 5082, 8475, 13056, 18987, 26430, 35547, 46500, 59451, 74562, 91995, 111912, 134475, 159846, 188187, 219660, 254427, 292650, 334491, 380112, 429675, 483342, 541275, 603636, 670587, 742290, 818907, 900600, 987531, 1079862
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Row 6 of A221596.

Examples

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

Links

Crossrefs

Cf. A221596.

Formula

Empirical: a(n) = 27*n^3 + 108*n^2 - 252*n + 267 for n>3.
Conjectures from Colin Barker, Aug 09 2018: (Start)
G.f.: x*(64 + 137*x + 22*x^2 - 23*x^3 - 26*x^4 - 10*x^5 - 2*x^6) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>7.
(End)

A221599 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less.

Original entry on oeis.org

128, 1113, 4240, 11011, 22912, 41401, 67936, 103975, 150976, 210397, 283696, 372331, 477760, 601441, 744832, 909391, 1096576, 1307845, 1544656, 1808467, 2100736, 2422921, 2776480, 3162871, 3583552, 4039981, 4533616, 5065915, 5638336
Offset: 1

Views

Author

R. H. Hardin, Jan 20 2013

Keywords

Comments

Row 7 of A221596.

Examples

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

Links

Crossrefs

Cf. A221596.

Formula

Empirical: a(n) = 243*n^3 - 351*n^2 + 237*n + 127 for n>2.
Conjectures from Colin Barker, Aug 09 2018: (Start)
G.f.: x*(128 + 601*x + 556*x^2 + 217*x^3 - 16*x^4 - 28*x^5) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
(End)
Showing 1-8 of 8 results.

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