A268261 -id:A268261 - cp's OEIS frontend

A268254 Number of length-(n+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

3, 17, 143, 1610, 22710, 384605, 7594224, 171161319, 4333369912, 121706300672, 3754131927947, 126136021943207, 4584723067123764, 179223541390399501, 7497293121634632330, 334153612151475666156, 15807274255300507355559

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

Diagonal of A268261.

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

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

Cf. A268261.

A268255 Number of length-(n+1) 0..2 arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

7, 17, 42, 106, 273, 717, 1918, 5218, 14413, 40349, 114282, 326938, 943257, 2740797, 8010982, 23529346, 69385813, 205282157, 608959218, 1810358938, 5391414273, 16078923309, 48007516942, 143470822498, 429083952157, 1284051486077

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

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

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

Column 2 of A268261.

Empirical: a(n) = 7*a(n-1) - 15*a(n-2) + 7*a(n-3) + 6*a(n-4).
Conjectures from Colin Barker, Jan 11 2019: (Start)
G.f.: x*(7 - 32*x + 28*x^2 + 18*x^3) / ((1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)).
a(n) = 2^n + 3^n/2 + (3/4-1/sqrt(2))*(1-sqrt(2))^n + (3/4+1/sqrt(2))*(1+sqrt(2))^n.
(End)

A268256 Number of length-(n+1) 0..3 arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

13, 43, 143, 479, 1616, 5492, 18804, 64869, 225483, 789747, 2787100, 9910252, 35501416, 128109313, 465606659, 1704022367, 6278399432, 23282368196, 86873186508, 326055377709, 1230562324251, 4668500002491, 17797745988388

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

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

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

Column 3 of A268261.

Empirical: a(n) = 13*a(n-1) - 60*a(n-2) + 105*a(n-3) - 11*a(n-4) - 94*a(n-5) - 24*a(n-6).

Empirical g.f.: x*(13 - 126*x + 364*x^2 - 165*x^3 - 403*x^4 - 96*x^5) / ((1 - 3*x)*(1 - 4*x)*(1 - 3*x - x^2)*(1 - 3*x - 2*x^2)). - Colin Barker, Jan 11 2019

A268257 Number of length-(n+1) 0..4 arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

21, 89, 378, 1610, 6877, 29461, 126591, 545627, 2359152, 10233188, 44533546, 194450722, 851923695, 3745257911, 16522347429, 73145533817, 324971178262, 1448957138290, 6483809640888, 29119030669064, 131250471466965

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

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

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

Column 4 of A268261.

Empirical: a(n) = 21*a(n-1) - 170*a(n-2) + 634*a(n-3) - 899*a(n-4) - 401*a(n-5) + 1310*a(n-6) + 826*a(n-7) + 120*a(n-8).

Empirical g.f.: x*(21 - 352*x + 2079*x^2 - 4512*x^3 - 220*x^4 + 7524*x^5 + 4261*x^6 + 600*x^7) / ((1 - 4*x)*(1 - 5*x)*(1 - 4*x - x^2)*(1 - 4*x - 2*x^2)*(1 - 4*x - 3*x^2)). - Colin Barker, Jan 13 2019

A268258 Number of length-(n+1) 0..5 arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

31, 161, 837, 4357, 22710, 118530, 619490, 3242265, 16993552, 89197862, 468891563, 2468601733, 13016765331, 68745010766, 363645146551, 1926748983131, 10225750976768, 54362543336048, 289501143028324, 1544393456553619

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

Column 5 of A268261.

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

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

Cf. A268261.

Empirical: a(n) = 31*a(n-1) -390*a(n-2) +2490*a(n-3) -7960*a(n-4) +8610*a(n-5) +11775*a(n-6) -18175*a(n-7) -22024*a(n-8) -7236*a(n-9) -720*a(n-10)

A268259 Number of length-(n+1) 0..6 arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

43, 265, 1634, 10082, 62249, 384605, 2377935, 14712729, 91096234, 564452368, 3500093507, 21720172553, 134891317195, 838393028557, 5215069599851, 32465881779821, 202280863699652, 1261388175969986, 7872540872887539

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

Column 6 of A268261.

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

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

Cf. A268261.

Empirical: a(n) = 43*a(n-1) -777*a(n-2) +7545*a(n-3) -41215*a(n-4) +115171*a(n-5) -81663*a(n-6) -274113*a(n-7) +244616*a(n-8) +557626*a(n-9) +307440*a(n-10) +67488*a(n-11) +5040*a(n-12)

A268260 Number of length-(n+1) 0..7 arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

57, 407, 2907, 20771, 148468, 1061632, 7594224, 54345509, 389060724, 2786424182, 19964380499, 143102062257, 1026171833136, 7361751375225, 52836226761762, 379380311345241, 2725291071400498, 19586141747713834, 140826889434423348

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

Column 7 of A268261.

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

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

Cf. A268261.

Empirical: a(n) = 57*a(n-1) -1400*a(n-2) +19187*a(n-3) -157759*a(n-4) +765212*a(n-5) -1872339*a(n-6) +503475*a(n-7) +6299972*a(n-8) -2706851*a(n-9) -14207501*a(n-10) -11689832*a(n-11) -4172972*a(n-12) -680688*a(n-13) -40320*a(n-14)

A268262 Number of length-(3+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

9, 42, 143, 378, 837, 1634, 2907, 4818, 7553, 11322, 16359, 22922, 31293, 41778, 54707, 70434, 89337, 111818, 138303, 169242, 205109, 246402, 293643, 347378, 408177, 476634, 553367, 639018, 734253, 839762, 956259, 1084482, 1225193

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

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

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

Row 3 of A268261.

Empirical: a(n) = n^4 + n^3 + 3*n^2 + 2*n + 2.
Conjectures from Colin Barker, Jan 13 2019: (Start)
G.f.: x*(9 - 3*x + 23*x^2 - 7*x^3 + 2*x^4) / (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)

A268263 Number of length-(4+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

17, 106, 479, 1610, 4357, 10082, 20771, 39154, 68825, 114362, 181447, 276986, 409229, 587890, 824267, 1131362, 1524001, 2018954, 2635055, 3393322, 4317077, 5432066, 6766579, 8351570, 10220777, 12410842, 14961431, 17915354, 21318685

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

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

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

Row 4 of A268261.

Empirical: a(n) = n^5 + n^4 + 4*n^3 + 3*n^2 + 6*n + 2.
Conjectures from Colin Barker, Jan 13 2019: (Start)
G.f.: x*(17 + 4*x + 98*x^2 - 14*x^3 + 17*x^4 - 2*x^5) / (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)

A268264 Number of length-(5+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

Original entry on oeis.org

33, 273, 1616, 6877, 22710, 62249, 148468, 318261, 627242, 1155265, 2012664, 3347213, 5351806, 8272857, 12419420, 18173029, 25998258, 36454001, 50205472, 68036925, 90865094, 119753353, 155926596, 200786837, 255929530, 323160609

Offset: 1

R. H. Hardin, Jan 29 2016

nonn

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

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

Row 5 of A268261.

Empirical: a(n) = n^6 + n^5 + 5*n^4 + 4*n^3 + 12*n^2 + 6*n + 5 for n>1.
Conjectures from Colin Barker, Jan 13 2019: (Start)
G.f.: x*(33 + 42*x + 398*x^2 + 143*x^3 + 107*x^4 - 2*x^5 - 2*x^6 + x^7) / (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>8.
(End)

cp's OEIS Frontend

A268254 Number of length-(n+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A268255 Number of length-(n+1) 0..2 arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268256 Number of length-(n+1) 0..3 arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268257 Number of length-(n+1) 0..4 arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268258 Number of length-(n+1) 0..5 arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A268259 Number of length-(n+1) 0..6 arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A268260 Number of length-(n+1) 0..7 arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A268262 Number of length-(3+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268263 Number of length-(4+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A268264 Number of length-(5+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

Views

Author

Keywords