A269467 -id:A269467 - cp's OEIS frontend

A269461 Number of length-n 0..2 arrays with no repeated value equal to the previous repeated value.

3, 9, 24, 66, 174, 462, 1206, 3150, 8166, 21150, 54582, 140718, 362118, 931134, 2391894, 6141006, 15757734, 40420062, 103647606, 265721070, 681097926, 1745555070, 4473092502, 11461604238, 29366557158, 75238139934, 192754700214

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

Column 2 of A269467.

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

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

Cf. A269467.

Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - 8*a(n-3).
Conjectures from Colin Barker, Mar 21 2018: (Start)
G.f.: 3*x*(1 - 3*x^2) / ((1 - 2*x)*(1 - x - 4*x^2)).
a(n) = 2^(-4-n)*(-51*4^(1+n) + (255-57*sqrt(17))*(1-sqrt(17))^n + 3*(1+sqrt(17))^n*(85+19*sqrt(17))) / 17.
(End)

A269460 Number of length-n 0..n arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

2, 9, 60, 580, 7170, 108402, 1934856, 39808584, 927352710, 24123618310, 693066874236, 21793557008028, 744461976979994, 27451268150267850, 1086741065393740560, 45971289976043485456, 2069440771476789080334

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

Diagonal of A269467.

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

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

Cf. A269467.

A269462 Number of length-n 0..3 arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

4, 16, 60, 228, 852, 3180, 11796, 43644, 160980, 592572, 2177268, 7988700, 29277204, 107195196, 392179380, 1433907228, 5240022612, 19140884220, 69894090996, 255150047964, 931214323860, 3397977981372, 12397189043508, 45224087388060

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Column 3 of A269467.

Empirical: a(n) = 5*a(n-1) - 18*a(n-3).
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: 4*x*(1 - x - 5*x^2) / ((1 - 3*x)*(1 - 2*x - 6*x^2)).
a(n) = (-28*3^n + (49-17*sqrt(7))*(1-sqrt(7))^n + (1+sqrt(7))^n*(49+17*sqrt(7))) / 63.
(End)

A269463 Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

5, 25, 120, 580, 2780, 13300, 63420, 301780, 1433180, 6795700, 32180220, 152216980, 719335580, 3396714100, 16028713020, 75595396180, 356358069980, 1679206088500, 7909957661820, 37249421039380, 175371521796380, 825484323238900

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Column 4 of A269467.

Empirical: a(n) = 7*a(n-1) - 4*a(n-2) - 32*a(n-3).

Empirical g.f.: 5*x*(1 - 2*x - 7*x^2) / ((1 - 4*x)*(1 - 3*x - 8*x^2)). - Colin Barker, Jan 22 2019

A269464 Number of length-n 0..5 arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

6, 36, 210, 1230, 7170, 41730, 242370, 1405530, 8139570, 47082330, 272068770, 1570817130, 9062549970, 52251339930, 301095703170, 1734220430730, 9984459848370, 57463149169530, 330612722505570, 1901660018436330

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Column 5 of A269467.

Empirical: a(n) = 9*a(n-1) - 10*a(n-2) - 50*a(n-3).
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: 6*x*(1 - 3*x - 9*x^2) / ((1 - 5*x)*(1 - 4*x - 10*x^2)).
a(n) = (-84*5^n + (231-57*sqrt(14))*(2-sqrt(14))^n + 3*(2+sqrt(14))^n*(77+19*sqrt(14))) / 350.
(End)

A269465 Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

7, 49, 336, 2310, 15834, 108402, 741090, 5060706, 34523202, 235304034, 1602555906, 10906971810, 74188793154, 504367206882, 3427339028610, 23280526483746, 158079249910722, 1073053862250594, 7281968079533826, 49404973360789410

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Column 6 of A269467.

Empirical: a(n) = 11*a(n-1) -18*a(n-2) -72*a(n-3).
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: 7*x*(1 - 4*x - 11*x^2) / ((1 - 6*x)*(1 - 5*x - 12*x^2)).
a(n) = (7/657)*2^(-4-n) * (-73*3^n*4^(1+n) + (949-103*sqrt(73))*(5-sqrt(73))^n + (5+sqrt(73))^n*(949+103*sqrt(73))).
(End)

A269466 Number of length-n 0..7 arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

8, 64, 504, 3976, 31304, 246232, 1934856, 15190840, 119174216, 934305400, 7320389832, 57325443448, 448697920328, 3510562344184, 27455875247304, 214658236385656, 1677757456358984, 13109740539632632, 102412911071378376

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Column 7 of A269467.

Empirical: a(n) = 13*a(n-1) -28*a(n-2) -98*a(n-3).
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: 8*x*(1 - 5*x - 13*x^2) / ((1 - 7*x)*(1 - 6*x - 14*x^2)).
a(n) = 2*(-92*7^n + (345-67*sqrt(23))*(3-sqrt(23))^n + (3+sqrt(23))^n*(345+67*sqrt(23))) / 1127.
(End)

A269468 Number of length-4 0..n arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

10, 66, 228, 580, 1230, 2310, 3976, 6408, 9810, 14410, 20460, 28236, 38038, 50190, 65040, 82960, 104346, 129618, 159220, 193620, 233310, 278806, 330648, 389400, 455650, 530010, 613116, 705628, 808230, 921630, 1046560, 1183776, 1334058

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Row 4 of A269467.

Empirical: a(n) = n^4 + 4*n^3 + 4*n^2 + n.
Conjectures from Colin Barker, Jan 23 2019: (Start)
G.f.: 2*x*(5 + 8*x - x^2) / (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)

A269469 Number of length-5 0..n arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

14, 174, 852, 2780, 7170, 15834, 31304, 56952, 97110, 157190, 243804, 364884, 529802, 749490, 1036560, 1405424, 1872414, 2455902, 3176420, 4056780, 5122194, 6400394, 7921752, 9719400, 11829350, 14290614, 17145324, 20438852, 24219930

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Row 5 of A269467.

Empirical: a(n) = n^5 + 5*n^4 + 7*n^3 + 2*n^2 - n.
Conjectures from Colin Barker, Jan 23 2019: (Start)
G.f.: 2*x*(7 + 45*x + 9*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)

A269470 Number of length-6 0..n arrays with no repeated value equal to the previous repeated value.

Original entry on oeis.org

22, 462, 3180, 13300, 41730, 108402, 246232, 505800, 960750, 1713910, 2904132, 4713852, 7377370, 11189850, 16517040, 23805712, 33594822, 46527390, 63363100, 84991620, 112446642, 146920642, 189780360, 242583000, 307093150, 385300422

Offset: 1

R. H. Hardin, Feb 27 2016

nonn

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

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

Row 6 of A269467.

Empirical: a(n) = n^6 + 6*n^5 + 11*n^4 + 4*n^3 - n^2 + n.
Conjectures from Colin Barker, Jan 23 2019: (Start)
G.f.: 2*x*(11 + 154*x + 204*x^2 - 14*x^3 + 5*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)

cp's OEIS Frontend

A269461 Number of length-n 0..2 arrays with no repeated value equal to the previous repeated value.

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A269460 Number of length-n 0..n arrays with no repeated value equal to the previous repeated value.

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A269462 Number of length-n 0..3 arrays with no repeated value equal to the previous repeated value.

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A269463 Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value.

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A269464 Number of length-n 0..5 arrays with no repeated value equal to the previous repeated value.

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A269465 Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value.

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A269466 Number of length-n 0..7 arrays with no repeated value equal to the previous repeated value.

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A269468 Number of length-4 0..n arrays with no repeated value equal to the previous repeated value.

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A269469 Number of length-5 0..n arrays with no repeated value equal to the previous repeated value.

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A269470 Number of length-6 0..n arrays with no repeated value equal to the previous repeated value.

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