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 1-9 of 9 results.

A221677 Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

0, 2, 5, 14, 40, 113, 320, 906, 2565, 7262, 20560, 58209, 164800, 466578, 1320965, 3739886, 10588280, 29977297, 84871040, 240284954, 680289285, 1926019518, 5452902560, 15438133441, 43708091520, 123745352482, 350345021445
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Column 2 of A221683.

Examples

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

Links

Formula

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

A221678 Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

0, 2, 5, 20, 68, 241, 844, 2966, 10413, 36568, 128408, 450913, 1583400, 5560186, 19524853, 68562444, 240760252, 845440977, 2968805844, 10425101678, 36608235997, 128551546480, 451414815600, 1585164405441, 5566379537040
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Column 3 of A221683.

Examples

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

Links

Formula

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

A221679 Number of 0..4 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

0, 2, 5, 26, 100, 418, 1692, 6932, 28288, 115604, 472188, 1929012, 7880012, 32190588, 131500508, 537189116, 2194454252, 8964498844, 36620598988, 149597691420, 611116954220, 2496455194876, 10198192807820, 41660325742812
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Column 4 of A221683.

Examples

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

Links

Formula

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

A221680 Number of 0..5 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

0, 2, 5, 32, 133, 636, 2856, 13169, 60120, 275632, 1261451, 5777107, 26449970, 121113272, 554546205, 2539172736, 11626346343, 53234805475, 243751618738, 1116090939600, 5110360772166, 23399338403512, 107140971422686
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Column 5 of A221683.

Examples

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

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.: x^2*(2 - 3*x + 6*x^2 + 2*x^3) / (1 - 4*x - 3*x^2 + 6*x^3 - 19*x^4 - 5*x^5 - x^6). - Colin Barker, Oct 19 2017

A221681 Number of 0..6 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

0, 2, 5, 38, 166, 891, 4326, 21985, 109567, 551027, 2759757, 13846871, 69418237, 348143326, 1745704167, 8754189034, 43898170484, 220132165897, 1103869189670, 5535451646119, 27757983230949, 139194805502163, 698004183274703
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Column 6 of A221683.

Examples

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

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*(2 - 3*x + 8*x^2 + 3*x^3 + 6*x^4 - x^5 + 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

A221682 Number of 0..7 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

0, 2, 5, 44, 199, 1182, 6102, 33710, 180382, 980490, 5289023, 28634131, 154747076, 837016897, 4525504274, 24472972752, 132331839901, 715586695597, 3869459738102, 20923925463760, 113144565987295, 611822365490334
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Column 7 of A221683.

Examples

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

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.: x^2*(2 - 5*x + 13*x^2 - 4*x^3 + 5*x^4 + 2*x^5 + 2*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

A221684 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

16, 40, 68, 100, 133, 166, 199, 232, 265, 298, 331, 364, 397, 430, 463, 496, 529, 562, 595, 628, 661, 694, 727, 760, 793, 826, 859, 892, 925, 958, 991, 1024, 1057, 1090, 1123, 1156, 1189, 1222, 1255, 1288, 1321, 1354, 1387, 1420, 1453, 1486, 1519, 1552, 1585
Offset: 1

Views

Author

R. H. Hardin Jan 22 2013

Keywords

Comments

Row 5 of A221683

Examples

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

Links

Formula

Empirical: a(n) = 33*n - 32 for n>3

A221685 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

32, 113, 241, 418, 636, 891, 1182, 1509, 1872, 2271, 2706, 3177, 3684, 4227, 4806, 5421, 6072, 6759, 7482, 8241, 9036, 9867, 10734, 11637, 12576, 13551, 14562, 15609, 16692, 17811, 18966, 20157, 21384, 22647, 23946, 25281, 26652, 28059, 29502, 30981
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Row 6 of A221683.

Examples

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

Links

Crossrefs

Cf. A221683.

Formula

Empirical: a(n) = 18*n^2 + 57*n - 99 for n>4.
Conjectures from Colin Barker, Aug 10 2018: (Start)
G.f.: x*(32 + 17*x - 2*x^2 + 2*x^3 - 8*x^4 - 4*x^5 - x^6) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)

A221686 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less, starting with 0.

Original entry on oeis.org

64, 320, 844, 1692, 2856, 4326, 6102, 8184, 10572, 13266, 16266, 19572, 23184, 27102, 31326, 35856, 40692, 45834, 51282, 57036, 63096, 69462, 76134, 83112, 90396, 97986, 105882, 114084, 122592, 131406, 140526, 149952, 159684, 169722, 180066, 190716
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2013

Keywords

Comments

Row 7 of A221683.

Examples

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

Links

Crossrefs

Cf. A221683.

Formula

Empirical: a(n) = 153*n^2 - 213*n + 96 for n>3.
Conjectures from Colin Barker, Aug 10 2018: (Start)
G.f.: 2*x*(32 + 64*x + 38*x^2 + 28*x^3 - 4*x^4 - 5*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)
Showing 1-9 of 9 results.

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