A212829 -id:A212829 - cp's OEIS frontend

A212823 Number of 0..2 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..2 order.

1, 2, 5, 12, 33, 90, 246, 672, 1836, 5016, 13704, 37440, 102288, 279456, 763488, 2085888, 5698752, 15569280, 42536064, 116210688, 317493504, 867408384, 2369803776, 6474424320, 17688456192, 48325761024, 132028434432, 360708390912

Offset: 1

R. H. Hardin, May 28 2012

nonn

Column 2 of A212829.

			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....1....0....1....1....1....0....1....1....1....1....1
..2....2....1....2....2....2....0....0....2....1....1....1....0....0....2....2
..1....0....0....2....2....0....1....2....0....1....2....2....2....0....0....0
..0....0....2....2....0....1....2....1....0....2....2....0....1....1....2....2
..0....1....0....0....1....1....2....0....0....0....0....0....0....2....2....2
..1....0....0....2....0....0....1....0....1....0....0....1....2....2....0....2
..1....0....1....2....0....2....2....0....1....0....2....0....1....0....1....0

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

Cf. A212829.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) for n>5.

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

A212824 Number of 0..3 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..3 order.

Original entry on oeis.org

1, 2, 5, 13, 43, 152, 559, 2091, 7882, 29809, 112895, 427824, 1621691, 6147791, 23307226, 88363077, 335007715, 1270107208, 4815336407, 18256317315, 69214939274, 262413734345, 994885963543, 3771899000928, 14300354743363

Offset: 1

R. H. Hardin, May 28 2012

nonn

Column 3 of A212829.

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

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

Cf. A212829.

Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4) for n>7.

Empirical g.f.: x*(1 + x + x^2)*(1 - 3*x - 2*x^2 + 2*x^3 + x^4) / ((1 - x - x^2)*(1 - 3*x - 3*x^2)). - Colin Barker, Jul 21 2018

A212825 Number of 0..4 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..4 order.

Original entry on oeis.org

1, 2, 5, 13, 44, 167, 695, 3070, 14074, 65958, 313098, 1497216, 7189646, 34606966, 166803484, 804596882, 3882748894, 18741593296, 90476092366, 436812623774, 2108996095916, 10182801139146, 49166003981046, 237391983175872

Offset: 1

R. H. Hardin, May 28 2012

nonn

Column 4 of A212829.

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

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

Cf. A212829.

Empirical: a(n) = 7*a(n-1) - 7*a(n-2) - 20*a(n-3) + 10*a(n-4) + 24*a(n-5) + 8*a(n-6) for n>9.

Empirical g.f.: x*(1 + x + x^2)*(1 - 6*x + 3*x^2 + 15*x^3 - 9*x^5 - 3*x^6) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x - 4*x^2)). - Colin Barker, Jul 21 2018

A212826 Number of 0..5 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..5 order.

Original entry on oeis.org

1, 2, 5, 13, 44, 168, 716, 3331, 16599, 87059, 473569, 2641428, 14982656, 85930423, 496412949, 2881216925, 16773626497, 97843056510, 571457023718, 3340356838651, 19535838889479, 114293073644447, 668811749036809, 3914263576403496

Offset: 1

R. H. Hardin, May 28 2012

nonn

Column 5 of A212829.

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

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

Cf. A212829.

Empirical: a(n) = 11*a(n-1) - 30*a(n-2) - 21*a(n-3) + 112*a(n-4) + 63*a(n-5) - 119*a(n-6) - 120*a(n-7) - 30*a(n-8) for n>11.

Empirical g.f.: x*(1 + x + x^2)*(1 - 10*x + 22*x^2 + 27*x^3 - 68*x^4 - 67*x^5 + 29*x^6 + 44*x^7 + 11*x^8) / ((1 - x - x^2)*(1 - 2*x - 2*x^2)*(1 - 3*x - 3*x^2)*(1 - 5*x - 5*x^2)). - Colin Barker, Jul 21 2018

A212827 Number of 0..6 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..6 order.

Original entry on oeis.org

1, 2, 5, 13, 44, 168, 717, 3359, 17055, 92749, 534071, 3220152, 20122695, 129180223, 845868450, 5618381653, 37699577379, 254789247816, 1730682217663, 11797467544723, 80618379435810, 551861368167305, 3782253874750807

Offset: 1

R. H. Hardin May 28 2012

nonn

Column 6 of A212829

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

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

Empirical: a(n) = 16*a(n-1) -79*a(n-2) +70*a(n-3) +361*a(n-4) -372*a(n-5) -964*a(n-6) +144*a(n-7) +1116*a(n-8) +720*a(n-9) +144*a(n-10) for n>13

A212828 Number of 0..7 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..7 order.

Original entry on oeis.org

1, 2, 5, 13, 44, 168, 717, 3360, 17091, 93492, 545670, 3372738, 21911216, 148486735, 1041923520, 7518618028, 55460237723, 416078640459, 3161904730760, 24261222270154, 187499556005523, 1456815538485716, 11363752138036864

Offset: 1

R. H. Hardin May 28 2012

nonn

Column 7 of A212829

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

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

Empirical: a(n) = 22*a(n-1) -168*a(n-2) +440*a(n-3) +421*a(n-4) -2898*a(n-5) -924*a(n-6) +7944*a(n-7) +5931*a(n-8) -6610*a(n-9) -10562*a(n-10) -5040*a(n-11) -840*a(n-12) for n>15

A212830 Number of 0..n arrays of length n+1 with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..n order.

Original entry on oeis.org

2, 5, 13, 44, 168, 717, 3360, 17092, 93538, 546873, 3396379, 22300885, 154193327, 1118804486, 8493592723, 67288261914, 554996479921, 4756036642107, 42266543239132, 388879705390976, 3698606881082199, 36312877059583874

Offset: 1

R. H. Hardin May 28 2012

nonn

Subdiagonal 1 of A212829

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

R. H. Hardin, Table of n, a(n) for n = 1..60

cp's OEIS Frontend

A212823 Number of 0..2 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..2 order.

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A212824 Number of 0..3 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..3 order.

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A212825 Number of 0..4 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..4 order.

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A212826 Number of 0..5 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..5 order.

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A212827 Number of 0..6 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..6 order.

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A212828 Number of 0..7 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..7 order.

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A212830 Number of 0..n arrays of length n+1 with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..n order.

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