A269619 -id:A269619 - cp's OEIS frontend

A269613 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

3, 9, 27, 78, 222, 624, 1740, 4824, 13320, 36672, 100752, 276384, 757344, 2073600, 5674176, 15520128, 42437760, 116014080, 317100288, 866621952, 2368230912, 6471278592, 17682164736, 48313178112, 132003268608, 360658059264

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

Column 2 of A269619.

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

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

Cf. A269619.

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

A269612 Number of length-n 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

2, 9, 64, 612, 7440, 110099, 1923796, 38800210, 887591878, 22714070251, 643030722208, 19954247152834, 673552866591198, 24570545121277999, 963253518328620796, 40387590591059009524, 1803427358679591518028

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

Diagonal of A269619.

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

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

Cf. A269619.

A269614 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

4, 16, 64, 249, 954, 3611, 13544, 50442, 186822, 688899, 2531406, 9275757, 33912330, 123759252, 450985950, 1641487455, 5969001906, 21688869249, 78760649178, 285872602590, 1037218320720, 3762161399673, 13642773106086, 49463937282915

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

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

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

Column 3 of A269619.

Empirical: a(n) = 12*a(n-1) - 51*a(n-2) + 81*a(n-3) - 3*a(n-4) - 63*a(n-5) - 24*a(n-6) - 9*a(n-7).

Empirical g.f.: x*(4 - 32*x + 76*x^2 - 27*x^3 - 54*x^4 - 22*x^5 - 7*x^6) / ((1 - 3*x)*(1 - 9*x + 24*x^2 - 9*x^3 - 24*x^4 - 9*x^5 - 3*x^6)). - Colin Barker, Jan 25 2019

A269615 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

5, 25, 125, 612, 2956, 14125, 66925, 314935, 1473779, 6865098, 31856590, 147352985, 679742085, 3128486473, 14370696813, 65902020548, 301787376436, 1380297559417, 6306497302225, 28787967919963, 131309246498679, 598532215284482

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

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

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

Column 4 of A269619.

Empirical: a(n) = 16*a(n-1) - 93*a(n-2) + 220*a(n-3) - 115*a(n-4) - 168*a(n-5) - 44*a(n-6) - 16*a(n-7).

Empirical g.f.: x*(5 - 55*x + 190*x^2 - 163*x^3 - 136*x^4 - 40*x^5 - 12*x^6) / ((1 - 4*x)*(1 - 12*x + 45*x^2 - 40*x^3 - 45*x^4 - 12*x^5 - 4*x^6)). - Colin Barker, Jan 25 2019

A269616 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

6, 36, 216, 1275, 7440, 43013, 246798, 1407232, 7982022, 45074673, 253574688, 1421878274, 7950451524, 44345786735, 246818403470, 1371136321437, 7604288654552, 42110933628975, 232895831580810, 1286536158378699

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

Column 5 of A269619.

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

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

Cf. A269619.

Empirical: a(n) = 35*a(n-1) -519*a(n-2) +4195*a(n-3) -19640*a(n-4) +51000*a(n-5) -56851*a(n-6) -16105*a(n-7) +50448*a(n-8) +35280*a(n-9) +12993*a(n-10) +3195*a(n-11) +444*a(n-12) +30*a(n-13)

A269617 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

7, 49, 343, 2370, 16218, 110099, 742487, 4979260, 33232924, 220896016, 1463045800, 9659912834, 63605763734, 417796855262, 2738396932202, 17913923467256, 116986307701928, 762789970679730, 4966685787053850, 32298201110078751

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

Column 6 of A269619.

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

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

Cf. A269619.

Empirical: a(n) = 48*a(n-1) -1001*a(n-2) +11802*a(n-3) -85449*a(n-4) +383292*a(n-5) -1000148*a(n-6) +1185936*a(n-7) +212633*a(n-8) -1064856*a(n-9) -732405*a(n-10) -264438*a(n-11) -65802*a(n-12) -10656*a(n-13) -1071*a(n-14) -54*a(n-15)

A269618 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

8, 64, 512, 4053, 31822, 248143, 1923796, 14840928, 113998742, 872397577, 6654286340, 50608816911, 383908730032, 2905532655620, 21944295375268, 165426094919204, 1244944198391978, 9354631892435631, 70193014149728040

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

Column 7 of A269619.

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

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

Cf. A269619.

Empirical: a(n) = 63*a(n-1) -1756*a(n-2) +28364*a(n-3) -291578*a(n-4) +1965390*a(n-5) -8566706*a(n-6) +22451548*a(n-7) -27837343*a(n-8) -2892449*a(n-9) +25243250*a(n-10) +17146752*a(n-11) +6127748*a(n-12) +1523522*a(n-13) +264748*a(n-14) +31542*a(n-15) +2437*a(n-16) +91*a(n-17)

A269620 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

15, 78, 249, 612, 1275, 2370, 4053, 6504, 9927, 14550, 20625, 28428, 38259, 50442, 65325, 83280, 104703, 130014, 159657, 194100, 233835, 279378, 331269, 390072, 456375, 530790, 613953, 706524, 809187, 922650, 1047645, 1184928, 1335279

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

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

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

Row 4 of A269619.

Empirical: a(n) = n^4 + 4*n^3 + 5*n^2 + 5*n.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: 3*x*(5 + x + 3*x^2 - x^3) / (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)

A269621 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

28, 222, 954, 2956, 7440, 16218, 31822, 57624, 97956, 158230, 245058, 366372, 531544, 751506, 1038870, 1408048, 1875372, 2459214, 3180106, 4060860, 5126688, 6405322, 7927134, 9725256, 11835700, 14297478, 17152722, 20446804, 24228456

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

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

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

Row 5 of A269619.

Empirical: a(n) = n^5 + 5*n^4 + 7*n^3 + 12*n^2 + 3*n.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: 2*x*(14 + 27*x + 21*x^2 + x^3 - 3*x^4) / (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)

A269622 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

Original entry on oeis.org

51, 624, 3611, 14125, 43013, 110099, 248143, 507521, 961625, 1712983, 2900099, 4705013, 7361581, 11164475, 16478903, 23751049, 33519233, 46425791, 63229675, 84819773, 112228949, 146648803, 189445151, 242174225, 306599593, 384709799

Offset: 1

R. H. Hardin, Mar 01 2016

nonn

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

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

Row 6 of A269619.

Empirical: a(n) = n^6 + 6*n^5 + 9*n^4 + 22*n^3 + 9*n^2 + 9*n - 7 for n>2.
Conjectures from Colin Barker, Jan 25 2019: (Start)
G.f.: x*(51 + 267*x + 314*x^2 + 167*x^3 - 86*x^4 + 17*x^5 - 14*x^6 + 5*x^7 - x^8) / (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>9.
(End)

cp's OEIS Frontend

A269613 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269612 Number of length-n 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269614 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269615 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269616 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269617 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269618 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269620 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269621 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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A269622 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.

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