A268944 -id:A268944 - cp's OEIS frontend

A268938 Number of length-n 0..2 arrays with no repeated value unequal to the previous repeated value plus one mod 2+1.

3, 9, 24, 63, 159, 396, 969, 2349, 5640, 13455, 31911, 75348, 177225, 415557, 971808, 2267631, 5281359, 12280860, 28518153, 66147165, 153274488, 354861711, 820976631, 1898144676, 4386240393, 10131006069, 23390390544, 53984735343

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Column 2 of A268944.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A268944.

Empirical: a(n) = 3*a(n-1) + a(n-2) - 6*a(n-3).

Empirical g.f.: 3*x*(1 - 2*x^2) / ((1 - 2*x)*(1 - x - 3*x^2)). - Colin Barker, Mar 21 2018

A268937 Number of length-n 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

Original entry on oeis.org

2, 9, 60, 565, 6834, 101192, 1773384, 35904789, 824720230, 21189902503, 602161461276, 18752026405918, 635032992414506, 23234614293228525, 913376056016994576, 38392537083966394681, 1718296926207889973454

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Diagonal of A268944.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A268944.

A268939 Number of length-n 0..3 arrays with no repeated value unequal to the previous repeated value plus one mod 3+1.

Original entry on oeis.org

4, 16, 60, 220, 788, 2780, 9684, 33404, 114292, 388444, 1312788, 4415548, 14790836, 49369628, 164279892, 545170172, 1804855540, 5962578652, 19661140116, 64722276796, 212738159924, 698312564636, 2289419181780, 7497612860540

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 3 of A268944.

Empirical: a(n) = 5*a(n-1) - 2*a(n-2) - 12*a(n-3).
Conjectures from Colin Barker, Jan 16 2019: (Start)
G.f.: 4*x*(1 - x - 3*x^2) / ((1 - 3*x)*(1 - 2*x - 4*x^2)).
a(n) = (-40*3^n + (25-11*sqrt(5))*(1-sqrt(5))^n + (1+sqrt(5))^n*(25+11*sqrt(5))) / 10.
(End)

A268940 Number of length-n 0..4 arrays with no repeated value unequal to the previous repeated value plus one mod 4+1.

Original entry on oeis.org

5, 25, 120, 565, 2615, 11950, 54045, 242365, 1079240, 4777225, 21038595, 92244790, 402898865, 1753806625, 7611458520, 32945585965, 142262759615, 612991045150, 2636186279445, 11317111447765, 48506655275240, 207603081203425

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 4 of A268944.

Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 20*a(n-3).

Empirical g.f.: 5*x*(1 - 2*x - 4*x^2) / ((1 - 4*x)*(1 - 3*x - 5*x^2)). - Colin Barker, Jan 17 2019

A268941 Number of length-n 0..5 arrays with no repeated value unequal to the previous repeated value plus one mod 5+1.

Original entry on oeis.org

6, 36, 210, 1206, 6834, 38322, 213042, 1175850, 6450402, 35200458, 191222994, 1034688474, 5579060610, 29989217034, 160755450546, 859578198138, 4585950964578, 24416800390890, 129760544069778, 688431162218202

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 5 of A268944.

Empirical: a(n) = 9*a(n-1) - 14*a(n-2) - 30*a(n-3).
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 6*x*(1 - 3*x - 5*x^2) / ((1 - 5*x)*(1 - 4*x - 6*x^2)).
a(n) = (-12*5^(1+n) + (35-11*sqrt(10))*(2-sqrt(10))^n + (2+sqrt(10))^n*(35+11*sqrt(10))) / 10.
(End)

A268942 Number of length-n 0..6 arrays with no repeated value unequal to the previous repeated value plus one mod 6+1.

Original entry on oeis.org

7, 49, 336, 2275, 15239, 101192, 667065, 4370261, 28480312, 184750699, 1193659551, 7684815880, 49319275649, 315627565757, 2014797616440, 12831930191171, 81554529162967, 517343926505224, 3276087952780041, 20712766946115685

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 6 of A268944.

Empirical: a(n) = 11*a(n-1) - 23*a(n-2) - 42*a(n-3).

Empirical g.f.: 7*x*(1 - 4*x - 6*x^2) / ((1 - 6*x)*(1 - 5*x - 7*x^2)). - Colin Barker, Jan 17 2019

A268943 Number of length-n 0..7 arrays with no repeated value unequal to the previous repeated value plus one mod 7+1.

Original entry on oeis.org

8, 64, 504, 3928, 30344, 232696, 1773384, 13443064, 101433800, 762265720, 5707893576, 42605289208, 317113497800, 2354253598072, 17437541654088, 128885063291896, 950791205063624, 7001691181273720, 51477520840048968

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Column 7 of A268944.

Empirical: a(n) = 13*a(n-1) - 34*a(n-2) - 56*a(n-3).
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 8*x*(1 - 5*x - 7*x^2) / ((1 - 7*x)*(1 - 6*x - 8*x^2)).
a(n) = (-272*7^n + (153-37*sqrt(17))*(3-sqrt(17))^n + (3+sqrt(17))^n*(153+37*sqrt(17))) / 34.
(End)

A268945 Number of length-4 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

Original entry on oeis.org

10, 63, 220, 565, 1206, 2275, 3928, 6345, 9730, 14311, 20340, 28093, 37870, 49995, 64816, 82705, 104058, 129295, 158860, 193221, 232870, 278323, 330120, 388825, 455026, 529335, 612388, 704845, 807390, 920731, 1045600, 1182753, 1332970

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

			Some solutions for n=9:
..9. .3. .4. .0. .0. .7. .3. .6. .2. .7. .3. .0. .7. .6. .5. .7
..2. .7. .5. .9. .0. .5. .4. .7. .8. .8. .9. .8. .0. .3. .7. .2
..6. .2. .3. .7. .8. .9. .9. .7. .3. .6. .6. .8. .8. .8. .9. .7
..2. .5. .2. .4. .9. .7. .3. .2. .5. .0. .2. .9. .7. .1. .1. .9

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 4 of A268944.

Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + n + 1.
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: x*(10 + 13*x + 5*x^2 - 5*x^3 + x^4) / (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>5.
(End)

A268946 Number of length-5 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

Original entry on oeis.org

14, 159, 788, 2615, 6834, 15239, 30344, 55503, 95030, 154319, 239964, 359879, 523418, 741495, 1026704, 1393439, 1858014, 2438783, 3156260, 4033239, 5094914, 6368999, 7885848, 9678575, 11783174, 14238639, 17087084, 20373863, 24147690

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

			Some solutions for n=9:
..4. .1. .5. .8. .9. .1. .8. .3. .2. .9. .6. .3. .4. .3. .2. .7
..4. .9. .9. .2. .5. .6. .2. .9. .2. .2. .9. .8. .9. .6. .9. .2
..5. .8. .5. .9. .9. .0. .7. .1. .8. .3. .9. .5. .9. .8. .8. .6
..8. .3. .8. .5. .0. .2. .0. .7. .2. .7. .6. .0. .8. .1. .1. .1
..6. .4. .0. .8. .6. .7. .4. .0. .4. .8. .9. .6. .5. .1. .3. .0

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 5 of A268944.

Empirical: a(n) = n^5 + 5*n^4 + 4*n^3 + 3*n^2 + 2*n - 1.
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: x*(14 + 75*x + 44*x^2 - 8*x^3 - 6*x^4 + x^5) / (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>6.
(End)

A268947 Number of length-6 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

Original entry on oeis.org

22, 396, 2780, 11950, 38322, 101192, 232696, 482490, 923150, 1656292, 2819412, 4593446, 7211050, 10965600, 16220912, 23421682, 33104646, 45910460, 62596300, 84049182, 111300002, 145538296, 188127720, 240622250, 304783102, 382596372

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Row 6 of A268944.

Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 + 6*n^3 + 3*n^2 - n + 2.
Conjectures from Colin Barker, Jan 17 2019: (Start)
G.f.: 2*x*(11 + 121*x + 235*x^2 + 18*x^3 - 19*x^4 - 7*x^5 + x^6) / (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>7.
(End)

cp's OEIS Frontend

A268938 Number of length-n 0..2 arrays with no repeated value unequal to the previous repeated value plus one mod 2+1.

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A268937 Number of length-n 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

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A268939 Number of length-n 0..3 arrays with no repeated value unequal to the previous repeated value plus one mod 3+1.

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A268940 Number of length-n 0..4 arrays with no repeated value unequal to the previous repeated value plus one mod 4+1.

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A268941 Number of length-n 0..5 arrays with no repeated value unequal to the previous repeated value plus one mod 5+1.

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A268942 Number of length-n 0..6 arrays with no repeated value unequal to the previous repeated value plus one mod 6+1.

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A268943 Number of length-n 0..7 arrays with no repeated value unequal to the previous repeated value plus one mod 7+1.

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A268945 Number of length-4 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

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A268946 Number of length-5 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

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A268947 Number of length-6 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.

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