A268956 -id:A268956 - cp's OEIS frontend

A268952 Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

1, 2, 4, 12, 40, 153, 634, 2785, 12634, 58409, 272738, 1280233, 6024682, 28383609, 133772018, 630473513, 2970963898, 13996752665, 65924951490, 310433985929, 1461486107146, 6879181490937, 32374728610962, 152339562845289

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

			Some solutions for n=8:
..0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0
..1. .0. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .0. .1. .1. .1
..2. .1. .1. .2. .2. .2. .1. .2. .0. .2. .0. .2. .1. .0. .0. .2
..1. .2. .2. .3. .1. .3. .2. .2. .2. .1. .2. .1. .0. .2. .2. .0
..3. .0. .1. .4. .2. .2. .1. .3. .1. .3. .0. .3. .1. .2. .3. .1
..4. .1. .3. .0. .0. .4. .2. .3. .1. .1. .3. .0. .2. .3. .4. .1
..2. .2. .4. .1. .1. .3. .1. .4. .3. .0. .3. .3. .2. .4. .2. .2
..0. .2. .0. .3. .0. .1. .0. .4. .2. .2. .1. .2. .1. .0. .1. .0

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

Column 4 of A268956.

Empirical: a(n) = 11*a(n-1) -31*a(n-2) -41*a(n-3) +268*a(n-4) -90*a(n-5) -692*a(n-6) +512*a(n-7) +576*a(n-8) -512*a(n-9) for n>11.

Empirical g.f.: x*(1 - 9*x + 13*x^2 + 71*x^3 - 154*x^4 - 197*x^5 + 483*x^6 + 210*x^7 - 546*x^8 - 24*x^9 + 192*x^10) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 2*x^2)*(1 - x - 4*x^2)*(1 - 3*x - 8*x^2)). - Colin Barker, Jan 17 2019

A268953 Number of length-n 0..5 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

1, 2, 4, 12, 40, 154, 655, 3045, 15124, 78930, 426289, 2355975, 13216982, 74856340, 426491859, 2438853865, 13977348104, 80210943670, 460646222293, 2646524858907, 15207848530170, 87395420173144, 502235483752631, 2886069610014893

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Column 5 of A268956.

			Some solutions for n=8
..0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0
..1. .1. .1. .1. .0. .1. .1. .0. .1. .1. .1. .1. .1. .1. .1. .0
..0. .2. .0. .0. .1. .2. .0. .1. .2. .1. .1. .2. .1. .0. .2. .1
..1. .3. .0. .2. .0. .0. .2. .2. .0. .2. .2. .2. .2. .1. .3. .2
..1. .3. .2. .0. .2. .2. .1. .2. .3. .0. .3. .3. .1. .1. .4. .1
..2. .4. .1. .1. .2. .3. .0. .3. .3. .3. .1. .1. .0. .0. .4. .0
..2. .0. .3. .0. .3. .2. .0. .1. .1. .4. .3. .2. .3. .2. .1. .3
..3. .4. .0. .0. .1. .1. .1. .0. .0. .3. .1. .0. .1. .0. .1. .0

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

Cf. A268956.

Empirical: a(n) = 18*a(n-1) -110*a(n-2) +170*a(n-3) +801*a(n-4) -2920*a(n-5) -662*a(n-6) +12700*a(n-7) -6980*a(n-8) -22928*a(n-9) +19192*a(n-10) +15120*a(n-11) -14400*a(n-12) for n>14

A268954 Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

1, 2, 4, 12, 40, 154, 656, 3073, 15579, 84572, 485726, 2918103, 18146537, 115772922, 752410412, 4954432229, 32923518967, 220172576536, 1478770322954, 9961340359315, 67235635905765, 454423768826774, 3074025717951560

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Column 6 of A268956.

			Some solutions for n=8
..0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0. .0
..1. .1. .1. .1. .1. .0. .0. .1. .1. .1. .1. .1. .1. .1. .1. .1
..2. .2. .2. .0. .2. .1. .1. .2. .2. .2. .2. .0. .2. .2. .2. .2
..3. .0. .3. .1. .3. .0. .2. .3. .3. .3. .1. .2. .1. .2. .0. .3
..2. .2. .0. .2. .4. .1. .1. .0. .2. .3. .3. .1. .2. .1. .3. .4
..3. .3. .1. .3. .0. .2. .0. .1. .1. .0. .1. .3. .3. .0. .4. .2
..3. .0. .3. .1. .5. .3. .2. .3. .3. .0. .2. .2. .2. .1. .3. .1
..4. .0. .0. .1. .0. .2. .3. .1. .1. .3. .3. .2. .2. .2. .4. .4

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

Cf. A268956.

Empirical: a(n) = 27*a(n-1) -280*a(n-2) +1258*a(n-3) -781*a(n-4) -13833*a(n-5) +39878*a(n-6) +32104*a(n-7) -261136*a(n-8) +111564*a(n-9) +754544*a(n-10) -663920*a(n-11) -1052352*a(n-12) +1135872*a(n-13) +580608*a(n-14) -663552*a(n-15) for n>17

A268955 Number of length-n 0..7 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

1, 2, 4, 12, 40, 154, 656, 3074, 15615, 85314, 497262, 3068890, 19899645, 134520386, 940841796, 6760952170, 49617422739, 370013347266, 2792665457338, 21266237427018, 163008076378489, 1255477313622210, 9703388630792784

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Column 7 of A268956.

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

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

Cf. A268956.

Empirical: a(n) = 38*a(n-1) -593*a(n-2) +4702*a(n-3) -17263*a(n-4) -4158*a(n-5) +265149*a(n-6) -681270*a(n-7) -916836*a(n-8) +6212496*a(n-9) -2473032*a(n-10) -24948000*a(n-11) +25941088*a(n-12) +53418784*a(n-13) -73975984*a(n-14) -60452512*a(n-15) +93916672*a(n-16) +28869120*a(n-17) -45158400*a(n-18) for n>20

A268957 Number of length-(n+3) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

5, 29, 138, 634, 3045, 15579, 85314, 498408, 3092383, 20286281, 140153290, 1016261974, 7710988251, 61062381647, 503482376776, 4313580705556, 38328590370571, 352618807558797, 3353663977088616, 32927374589861042

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Subdiagonal 3 of A268956.

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

R. H. Hardin, Table of n, a(n) for n = 1..119

Cf. A268956.

A268958 Number of length-(n+4) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

7, 77, 499, 2785, 15124, 84572, 497262, 3090688, 20283861, 140149935, 1016257437, 7710982245, 61062373842, 503482366796, 4313580692976, 38328590354914, 352618807539531, 3353663977065151, 32927374589832727, 333319732348780989

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Subdiagonal 4 of A268956.

			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. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1. .1
..2. .1. .1. .2. .2. .1. .2. .1. .2. .2. .2. .2. .2. .0. .0. .2
..3. .2. .2. .2. .2. .0. .2. .2. .1. .0. .3. .0. .0. .0. .1. .0
..1. .0. .3. .3. .0. .2. .1. .3. .2. .1. .4. .1. .2. .2. .2. .3
..1. .1. .2. .2. .3. .3. .1. .1. .3. .3. .2. .3. .0. .3. .0. .3
..3. .3. .1. .0. .1. .1. .0. .0. .2. .0. .0. .3. .0. .2. .1. .1
..2. .4. .1. .3. .4. .2. .2. .1. .2. .2. .4. .2. .3. .3. .1. .0
..0. .3. .2. .0. .0. .4. .2. .2. .3. .2. .0. .0. .2. .4. .3. .4
..1. .5. .1. .4. .0. .1. .3. .2. .4. .3. .2. .4. .2. .5. .2. .2

R. H. Hardin, Table of n, a(n) for n = 1..118

Cf. A268956.

A268959 Number of length-(n+5) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

11, 201, 1830, 12634, 78930, 485726, 3068890, 20245176, 140084705, 1016152035, 7710817964, 61062125594, 503482001606, 4313580168256, 38328589616502, 352618806519480, 3353663975679253, 32927374587977757, 333319732346331654

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Subdiagonal 5 of A268956.

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

R. H. Hardin, Table of n, a(n) for n = 1..117

Cf. A268956.

A268960 Number of length-(n+6) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

15, 525, 6723, 58409, 426289, 2918103, 19899645, 139354433, 1014707218, 7708112426, 61057289906, 503473697674, 4313566395798, 38328567460364, 352618771825166, 3353663922642364, 32927374508631249, 333319732229912935

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Subdiagonal 6 of A268956.

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

R. H. Hardin, Table of n, a(n) for n = 1..116

Cf. A268956.

A268961 Number of length-(n+7) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

Original entry on oeis.org

23, 1361, 24714, 272738, 2355975, 18146537, 134520386, 1002621328, 7680218714, 60997066270, 503350821180, 4313327580676, 38328122520204, 352617973045358, 3353662534979250, 32927372167566264, 333319728382967773

Offset: 1

R. H. Hardin, Feb 16 2016

nonn

Subdiagonal 7 of A268956.

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

R. H. Hardin, Table of n, a(n) for n = 1..115

Cf. A268956.

cp's OEIS Frontend

A268952 Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268953 Number of length-n 0..5 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268954 Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268955 Number of length-n 0..7 arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268957 Number of length-(n+3) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268958 Number of length-(n+4) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268959 Number of length-(n+5) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268960 Number of length-(n+6) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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A268961 Number of length-(n+7) 0..n arrays with no repeated value equal to the previous repeated value, with new values introduced in sequential order.

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