A269537 -id:A269537 - cp's OEIS frontend

A269532 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than one.

4, 16, 60, 222, 804, 2878, 10192, 35812, 125012, 434110, 1500912, 5170626, 17758812, 60837880, 207965356, 709583398, 2417278172, 8223508510, 27943213944, 94853465148, 321696510276, 1090199408374, 3692112980824, 12496559933794

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

Column 3 of A269537.

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

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

Cf. A269537.

Empirical: a(n) = 7*a(n-1) - 9*a(n-2) - 23*a(n-3) + 31*a(n-4) + 33*a(n-5).

Empirical g.f.: 2*x*(2 - 6*x - 8*x^2 + 19*x^3 + 17*x^4) / ((1 - 3*x)*(1 - 4*x - 3*x^2 + 14*x^3 + 11*x^4)). - Colin Barker, Mar 21 2018

A269530 Number of length-n 0..n arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

2, 9, 60, 568, 6890, 102202, 1792788, 36313762, 834223586, 21432797300, 608957461160, 18959064989614, 641864430972850, 23477543114153020, 922643768971802072, 38770277525975117782, 1734684393525837427074

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

Diagonal of A269537.

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

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

Cf. A269537.

A269531 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

3, 9, 24, 64, 164, 418, 1048, 2614, 6468, 15942, 39120, 95734, 233660, 569230, 1384408, 3362686, 8158932, 19778982, 47913504, 115999462, 280698860, 678970558, 1641785704, 3968834446, 9592037508, 23178077334, 55998523824, 135275792374

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

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

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

Column 2 of A269537.

Empirical: a(n) = 4*a(n-1) - a(n-2) - 10*a(n-3) + 6*a(n-4) + 4*a(n-5).

Empirical g.f.: x*(3 - 3*x - 9*x^2 + 7*x^3 + 4*x^4) / ((1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x^2)). - Colin Barker, Jan 23 2019

A269533 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

5, 25, 120, 568, 2648, 12214, 55836, 253418, 1143256, 5131592, 22934652, 102124670, 453300160, 2006497722, 8860136576, 39040820448, 171705037456, 753921273870, 3305432501828, 14473039186090, 63296720868120, 276532411704016

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

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

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

Column 4 of A269537.

Empirical: a(n) = 14*a(n-1) - 65*a(n-2) + 80*a(n-3) + 163*a(n-4) - 280*a(n-5) - 208*a(n-6).

Empirical g.f.: x*(5 - 45*x + 95*x^2 + 113*x^3 - 319*x^4 - 213*x^5) / ((1 - 4*x)^2*(1 - 6*x + x^2 + 24*x^3 + 13*x^4)). - Colin Barker, Jan 23 2019

A269534 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

6, 36, 210, 1210, 6890, 38878, 217714, 1211476, 6705102, 36939610, 202696070, 1108372980, 6042240154, 32850033316, 178168192702, 964256946776, 5208585411106, 28086302736278, 151213240334794, 812960203889834

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

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

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

Column 5 of A269537.

Empirical: a(n) = 17*a(n-1) - 92*a(n-2) + 96*a(n-3) + 493*a(n-4) - 533*a(n-5) - 1521*a(n-6) - 695*a(n-7).

Empirical g.f.: 2*x*(3 - 33*x + 75*x^2 + 188*x^3 - 387*x^4 - 821*x^5 - 354*x^6) / ((1 - 5*x)*(1 - 12*x + 32*x^2 + 64*x^3 - 173*x^4 - 332*x^5 - 139*x^6)). - Colin Barker, Jan 23 2019

A269535 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

7, 49, 336, 2280, 15324, 102202, 677200, 4462414, 29265308, 191134204, 1243794600, 8068058218, 52186113316, 336696234188, 2167362918200, 13922979926042, 89273834257404, 571453869667592, 3652311182519800, 23309932135990218

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

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

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

Column 6 of A269537.

Empirical: a(n) = 26*a(n-1) - 246*a(n-2) + 896*a(n-3) + 123*a(n-4) - 6658*a(n-5) + 796*a(n-6) + 22824*a(n-7) + 23326*a(n-8) + 6924*a(n-9).

Empirical g.f.: x*(7 - 133*x + 784*x^2 - 674*x^3 - 6065*x^4 + 4181*x^5 + 26114*x^6 + 24478*x^7 + 7026*x^8) / ((1 - 6*x)*(1 - 20*x + 126*x^2 - 140*x^3 - 963*x^4 + 880*x^5 + 4484*x^6 + 4080*x^7 + 1154*x^8)). - Colin Barker, Jan 23 2019

A269536 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

8, 64, 504, 3934, 30464, 234358, 1792788, 13648124, 103462888, 781425950, 5882591244, 44155349024, 330570580264, 2469019630228, 18401868960784, 136886638563766, 1016473079300584, 7535834884502158, 55785961230032092

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

Column 7 of A269537.

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

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

Cf. A269537.

Empirical: a(n) = 31*a(n-1) -355*a(n-2) +1651*a(n-3) -870*a(n-4) -13188*a(n-5) +7883*a(n-6) +59449*a(n-7) +59366*a(n-8) +18088*a(n-9)

A269538 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

10, 64, 222, 568, 1210, 2280, 3934, 6352, 9738, 14320, 20350, 28104, 37882, 50008, 64830, 82720, 104074, 129312, 158878, 193240, 232890, 278344, 330142, 388848, 455050, 529360, 612414, 704872, 807418, 920760, 1045630, 1182784, 1333002

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

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

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

Row 4 of A269537.

Empirical: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n.
Conjectures from Colin Barker, Jan 24 2019: (Start)
G.f.: 2*x*(1 + x)*(5 + 2*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)

A269539 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

14, 164, 804, 2648, 6890, 15324, 30464, 55664, 95238, 154580, 240284, 360264, 523874, 742028, 1027320, 1394144, 1858814, 2439684, 3157268, 4034360, 5096154, 6370364, 7887344, 9680208, 11784950, 14240564, 17089164, 20376104, 24150098

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

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

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

Row 5 of A269537.

Empirical: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 2*n.
Conjectures from Colin Barker, Jan 24 2019: (Start)
G.f.: 2*x*(7 + 40*x + 15*x^2 + 2*x^3 - 4*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)

A269540 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than one.

Original entry on oeis.org

22, 418, 2878, 12214, 38878, 102202, 234358, 485038, 926854, 1661458, 2826382, 4602598, 7222798, 10980394, 16239238, 23444062, 33131638, 45942658, 62634334, 84093718, 111351742, 145597978, 188196118, 240700174, 304871398, 382695922

Offset: 1

R. H. Hardin, Feb 29 2016

nonn

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

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

Row 6 of A269537.

Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 6*n^2 + 6*n - 2.
Conjectures from Colin Barker, Jan 24 2019: (Start)
G.f.: 2*x*(11 + 132*x + 207*x^2 + 38*x^3 - 21*x^4 - 6*x^5 - x^6) / (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

A269532 Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than one.

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A269530 Number of length-n 0..n arrays with no repeated value differing from the previous repeated value by other than one.

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A269531 Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than one.

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A269533 Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than one.

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A269534 Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than one.

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A269535 Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than one.

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A269536 Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than one.

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A269538 Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than one.

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A269539 Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than one.

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A269540 Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than one.

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