A269776 -id:A269776 - cp's OEIS frontend

A269770 Number of length-n 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

2, 9, 64, 620, 7680, 115920, 2063880, 42342912, 983566800, 25515160000, 731128554024, 22934195241984, 781644611944014, 28761550510694400, 1136386416816000000, 47984229920230342656, 2156419762355192954760

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

Diagonal of A269776.

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

R. H. Hardin, Table of n, a(n) for n = 1..193

Cf. A269776.

A269771 Number of length-n 0..3 arrays with every repeated value unequal to the previous repeated value plus one mod 3+1.

Original entry on oeis.org

4, 16, 64, 252, 984, 3816, 14724, 56592, 216864, 829116, 3164184, 12058632, 45904644, 174598416, 663634944, 2521077372, 9573268824, 36340434216, 137913296004, 523277751312, 1985122823904, 7529850771516, 28558867923864

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

			Some solutions for n=8:
..1. .3. .2. .3. .3. .1. .2. .0. .2. .0. .3. .3. .3. .2. .3. .1
..0. .0. .1. .1. .2. .3. .0. .2. .3. .3. .3. .3. .0. .1. .0. .0
..1. .0. .3. .1. .3. .0. .3. .2. .0. .2. .0. .1. .1. .2. .1. .0
..2. .3. .3. .1. .3. .2. .1. .2. .2. .2. .1. .0. .0. .0. .0. .1
..3. .3. .3. .1. .1. .1. .2. .2. .0. .1. .1. .1. .3. .0. .1. .0
..1. .1. .1. .1. .1. .1. .3. .3. .2. .0. .0. .2. .0. .1. .1. .0
..3. .0. .0. .1. .3. .1. .0. .0. .2. .0. .3. .0. .0. .2. .1. .0
..0. .1. .2. .2. .2. .0. .3. .3. .3. .3. .2. .1. .0. .2. .2. .1

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

Column 3 of A269776.

Empirical: a(n) = 6*a(n-1) - 6*a(n-2) - 9*a(n-3).

Empirical g.f.: 4*x*(1 - 2*x - 2*x^2) / ((1 - 3*x)*(1 - 3*x - 3*x^2)). - Colin Barker, Jan 28 2019

A269772 Number of length-n 0..4 arrays with every repeated value unequal to the previous repeated value plus one mod 4+1.

Original entry on oeis.org

5, 25, 125, 620, 3060, 15040, 73680, 360000, 1755200, 8542720, 41519360, 201559040, 977556480, 4737433600, 22943846400, 111060664320, 537360220160, 2599052247040, 12567124705280, 60750607155200, 293614524825600

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

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

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

Column 4 of A269776.

Empirical: a(n) = 8*a(n-1) - 12*a(n-2) - 16*a(n-3).

Empirical g.f.: 5*x*(1 - 3*x - 3*x^2) / ((1 - 4*x)*(1 - 4*x - 4*x^2)). - Colin Barker, Jan 29 2019

A269773 Number of length-n 0..5 arrays with every repeated value unequal to the previous repeated value plus one mod 5+1.

Original entry on oeis.org

6, 36, 216, 1290, 7680, 45600, 270150, 1597500, 9432000, 55616250, 327585000, 1927725000, 11335143750, 66607312500, 391177125000, 2296246406250, 13473738750000, 79033031250000, 463449377343750, 2716989679687500

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

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

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

Column 5 of A269776.

Empirical: a(n) = 10*a(n-1) - 20*a(n-2) - 25*a(n-3).

Empirical g.f.: 6*x*(1 - 4*x - 4*x^2) / ((1 - 5*x)*(1 - 5*x - 5*x^2)). - Colin Barker, Jan 29 2019

A269774 Number of length-n 0..6 arrays with every repeated value unequal to the previous repeated value plus one mod 6+1.

Original entry on oeis.org

7, 49, 343, 2394, 16674, 115920, 804636, 5577768, 38621016, 267152256, 1846396944, 12751839072, 88012679328, 607126689792, 4186073691072, 28850627143296, 198768754154880, 1369007582681088, 9426405790368000, 64890966854407680

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

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

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

Column 6 of A269776.

Empirical: a(n) = 12*a(n-1) - 30*a(n-2) - 36*a(n-3).

Empirical g.f.: 7*x*(1 - 5*x - 5*x^2) / ((1 - 6*x)*(1 - 6*x - 6*x^2)). - Colin Barker, Jan 29 2019

A269775 Number of length-n 0..7 arrays with every repeated value unequal to the previous repeated value plus one mod 7+1.

Original entry on oeis.org

8, 64, 512, 4088, 32592, 259504, 2063880, 16398144, 130175360, 1032602872, 8185566032, 64850011184, 513508842504, 4064330589760, 32155606323456, 254314670475768, 2010717722177360, 15893207240651440, 125593338184358408

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

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

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

Column 7 of A269776.

Empirical: a(n) = 14*a(n-1) - 42*a(n-2) -49*a(n-3).

Empirical g.f.: 8*x*(1 - 6*x - 6*x^2) / ((1 - 7*x)*(1 - 7*x - 7*x^2)). - Colin Barker, Jan 29 2019

A269777 Number of length-5 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

Original entry on oeis.org

24, 222, 984, 3060, 7680, 16674, 32592, 58824, 99720, 160710, 248424, 370812, 537264, 758730, 1047840, 1419024, 1888632, 2475054, 3198840, 4082820, 5152224, 6434802, 7960944, 9763800, 11879400, 14346774, 17208072, 20508684, 24297360

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

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

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

Row 5 of A269776.

Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 7*n^2 + n.
Conjectures from Colin Barker, Jan 29 2019: (Start)
G.f.: 6*x*(4 + 13*x + 2*x^2 + x^3) / (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)

A269778 Number of length-6 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

Original entry on oeis.org

40, 624, 3816, 15040, 45600, 115920, 259504, 527616, 994680, 1764400, 2976600, 4814784, 7514416, 11371920, 16754400, 24110080, 33979464, 47007216, 63954760, 85713600, 113319360, 147966544, 191024016, 244051200, 308815000, 387307440

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

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

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

Row 6 of A269776.

Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 14*n^3 + 4*n^2.
Conjectures from Colin Barker, Jan 29 2019: (Start)
G.f.: 8*x*(5 + 43*x + 36*x^2 + 4*x^3 + 2*x^4) / (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)

A269779 Number of length-7 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

Original entry on oeis.org

66, 1740, 14724, 73680, 270150, 804636, 2063880, 4728384, 9915210, 19361100, 35650956, 62496720, 105071694, 170405340, 267843600, 409579776, 611261010, 892675404, 1278524820, 1799288400, 2492181846, 3402217500, 4583370264

Offset: 1

R. H. Hardin, Mar 04 2016

nonn

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

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

Row 7 of A269776.

Empirical: a(n) = n^7 + 7*n^6 + 21*n^5 + 25*n^4 + 11*n^3 + n^2.
Conjectures from Colin Barker, Jan 29 2019: (Start)
G.f.: 6*x*(11 + 202*x + 442*x^2 + 152*x^3 + 27*x^4 + 6*x^5) / (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>8.
(End)

cp's OEIS Frontend

A269770 Number of length-n 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

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A269771 Number of length-n 0..3 arrays with every repeated value unequal to the previous repeated value plus one mod 3+1.

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A269772 Number of length-n 0..4 arrays with every repeated value unequal to the previous repeated value plus one mod 4+1.

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A269773 Number of length-n 0..5 arrays with every repeated value unequal to the previous repeated value plus one mod 5+1.

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A269774 Number of length-n 0..6 arrays with every repeated value unequal to the previous repeated value plus one mod 6+1.

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A269775 Number of length-n 0..7 arrays with every repeated value unequal to the previous repeated value plus one mod 7+1.

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A269777 Number of length-5 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

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A269778 Number of length-6 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

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A269779 Number of length-7 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.

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