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 10 results.

A269672 Number of length-n 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

Original entry on oeis.org

2, 9, 60, 570, 6918, 102606, 1799256, 36430614, 836599530, 21486777246, 610316761236, 18996711425718, 643003101276270, 23514920033329950, 923967843215031600, 38820647241658051158, 1736732998701525266514
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Comments

Diagonal of A269678.

Examples

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

Links

Crossrefs

Cf. A269678.

A269673 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 3+1.

Original entry on oeis.org

4, 16, 60, 224, 820, 2976, 10700, 38224, 135780, 480176, 1691740, 5941824, 20814740, 72755776, 253836780, 884207024, 3075861700, 10687549776, 37098781820, 128668433824, 445930140660, 1544500542176, 5346546062860, 18499277662224
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

			Some solutions for n=9:
..3. .0. .2. .0. .2. .0. .1. .0. .1. .3. .2. .2. .1. .3. .0. .0
..1. .3. .0. .1. .0. .1. .3. .1. .3. .0. .1. .1. .3. .1. .2. .0
..0. .3. .1. .3. .0. .0. .0. .1. .2. .1. .3. .3. .0. .0. .1. .1
..2. .0. .2. .3. .1. .3. .3. .0. .0. .2. .2. .1. .3. .1. .3. .3
..3. .0. .2. .2. .3. .0. .2. .2. .0. .1. .2. .0. .0. .3. .3. .2
..3. .1. .1. .1. .1. .0. .0. .0. .1. .0. .0. .0. .0. .3. .2. .0
..0. .2. .0. .0. .0. .3. .3. .3. .1. .2. .2. .3. .3. .1. .1. .3
..0. .3. .2. .1. .2. .3. .1. .1. .0. .2. .1. .2. .2. .0. .3. .3
..3. .2. .3. .2. .1. .1. .1. .3. .1. .0. .2. .1. .1. .0. .2. .0

Links

Crossrefs

Column 3 of A269678.

Formula

Empirical: a(n) = 5*a(n-1) - a(n-2) - 15*a(n-3).
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 4*x*(1 - x - 4*x^2) / ((1 - 3*x)*(1 - 2*x - 5*x^2)).
a(n) = (-20*3^n + (18-7*sqrt(6))*(1-sqrt(6))^n + (1+sqrt(6))^n*(18+7*sqrt(6))) / 15.
(End)

A269674 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 4+1.

Original entry on oeis.org

5, 25, 120, 570, 2670, 12390, 57030, 260790, 1185990, 5368470, 24204390, 108756150, 487223430, 2177121750, 9706364070, 43188455670, 191830083270, 850727111190, 3767586342630, 16664819732790, 73630769405190, 325004395216470
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Column 4 of A269678.

Formula

Empirical: a(n) = 7*a(n-1) - 6*a(n-2) - 24*a(n-3).
Empirical g.f.: 5*x*(1 - 2*x - 5*x^2) / ((1 - 4*x)*(1 - 3*x - 6*x^2)). - Colin Barker, Jan 26 2019

A269675 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 5+1.

Original entry on oeis.org

6, 36, 210, 1212, 6918, 39156, 220050, 1229292, 6832518, 37810116, 208443090, 1145318172, 6274749318, 34288099476, 186935018130, 1017053643852, 5523244077318, 29944773691236, 162103912681170, 876339613438332
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Column 5 of A269678.

Formula

Empirical: a(n) = 9*a(n-1) - 13*a(n-2) - 35*a(n-3).
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 6*x*(1 - 3*x - 6*x^2) / ((1 - 5*x)*(1 - 4*x - 7*x^2)).
a(n) = (-924*5^n + (660-195*sqrt(11))*(2-sqrt(11))^n + 15*(2+sqrt(11))^n*(44+13*sqrt(11))) / 385.
(End)

A269676 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 6+1.

Original entry on oeis.org

7, 49, 336, 2282, 15358, 102606, 681254, 4499278, 29579382, 193688894, 1263866086, 8221560942, 53335049558, 345145632286, 2228595939654, 14361269047118, 92377858496182, 593235919318014, 3803941311320486, 24358026991712302
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Column 6 of A269678.

Formula

Empirical: a(n) = 11*a(n-1) - 22*a(n-2) - 48*a(n-3).
Empirical g.f.: 7*x*(1 - 4*x - 7*x^2) / ((1 - 6*x)*(1 - 5*x - 8*x^2)). - Colin Barker, Jan 26 2019

A269677 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 7+1.

Original entry on oeis.org

8, 64, 504, 3936, 30504, 234912, 1799256, 13716480, 104139336, 787814400, 5940850872, 44672407968, 335060917608, 2507328861024, 18723903210264, 139560051510336, 1038430145451144, 7714504288777152, 57228077709064056
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Column 7 of A269678.

Formula

Empirical: a(n) = 13*a(n-1) - 33*a(n-2) - 63*a(n-3).
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 8*x*(1 - 5*x - 8*x^2) / ((1 - 7*x)*(1 - 6*x - 9*x^2)).
a(n) = (-216*7^n + (140-98*sqrt(2))*(3-3*sqrt(2))^n + 14*(3*(1+sqrt(2)))^n*(10+7*sqrt(2))) / 63.
(End)

A269679 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

Original entry on oeis.org

10, 66, 224, 570, 1212, 2282, 3936, 6354, 9740, 14322, 20352, 28106, 37884, 50010, 64832, 82722, 104076, 129314, 158880, 193242, 232892, 278346, 330144, 388850, 455052, 529362, 612416, 704874, 807420, 920762, 1045632, 1182786, 1333004
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Row 4 of A269678.

Formula

Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n + 2 for n>1.
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 2*x*(5 + 8*x - 3*x^2 + 5*x^3 - 4*x^4 + x^5) / (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>6.
(End)

A269680 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

Original entry on oeis.org

14, 174, 820, 2670, 6918, 15358, 30504, 55710, 95290, 154638, 240348, 360334, 523950, 742110, 1027408, 1394238, 1858914, 2439790, 3157380, 4034478, 5096278, 6370494, 7887480, 9680350, 11785098, 14240718, 17089324, 20376270, 24150270
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Row 5 of A269678.

Formula

Empirical: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 + 4*n - 2 for n>1.
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 2*x*(7 + 45*x - 7*x^2 + 40*x^3 - 36*x^4 + 13*x^5 - 2*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>7.
(End)

A269681 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

Original entry on oeis.org

22, 462, 2976, 12390, 39156, 102606, 234912, 485766, 927780, 1662606, 2827776, 4604262, 7224756, 10982670, 16241856, 23447046, 33135012, 45946446, 62638560, 84098406, 111356916, 145603662, 188202336, 240706950, 304878756, 382703886
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Row 6 of A269678.

Formula

Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 + 6*n^2 + 6 for n>1.
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 2*x*(11 + 154*x + 102*x^2 + 245*x^3 - 239*x^4 + 126*x^5 - 46*x^6 + 7*x^7) / (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>8.
(End)

A269682 Number of length-7 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.

Original entry on oeis.org

30, 1206, 10700, 57030, 220050, 681254, 1799256, 4215510, 8995310, 17809110, 33159204, 58656806, 99354570, 162139590, 256191920, 393513654, 589533606, 863792630, 1240714620, 1750468230, 2429924354, 3323714406, 4485394440
Offset: 1

Views

Author

R. H. Hardin, Mar 03 2016

Keywords

Examples

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

Links

Crossrefs

Row 7 of A269678.

Formula

Empirical: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 + 8*n^3 + 10*n^2 + 12*n - 10 for n>1.
Conjectures from Colin Barker, Jan 26 2019: (Start)
G.f.: 2*x*(15 + 483*x + 946*x^2 + 1759*x^3 - 1013*x^4 + 617*x^5 - 376*x^6 + 101*x^7 - 12*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>9.
(End)
Showing 1-10 of 10 results.

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