A267471 -id:A267471 - cp's OEIS frontend

A267464 Number of length-n 0..n arrays with no following elements larger than the first repeated value.

2, 9, 58, 515, 5921, 83972, 1418740, 27838701, 622347697, 15615978774, 434592601906, 13284763035843, 442468160695185, 15948347001674856, 618492693332510536, 25678060436644303705, 1136319246969590031009

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Diagonal of A267471.

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

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

Cf. A267471.

A267465 Number of length-n 0..2 arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

3, 9, 24, 62, 160, 418, 1112, 3018, 8352, 23522, 67240, 194554, 568304, 1672146, 4946808, 14692970, 43767616, 130647490, 390566216, 1168815066, 3500415888, 10488664754, 31439779864, 94264813642, 282681194720, 847808703138

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Column 2 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4).
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(3 - 15*x + 21*x^2 - 7*x^3) / ((1 - x)*(1 - 2*x)^2*(1 - 3*x)).
a(n) = 2^n + 3^(n-1) + 2^(n-2)*(n+1) - 1.
(End)

A267466 Number of length-n 0..3 arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

4, 16, 58, 204, 712, 2490, 8770, 31200, 112300, 409254, 1510102, 5638956, 21290368, 81183858, 312262954, 1210023672, 4718194516, 18492663102, 72787129726, 287468548548, 1138446338344, 4518338475786, 17963524388818, 71514144464784

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Column 3 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = 13*a(n-1) -65*a(n-2) +155*a(n-3) -174*a(n-4) +72*a(n-5).
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: 2*x*(2 - 18*x + 55*x^2 - 65*x^3 + 23*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)^2*(1 - 4*x)).
a(n) = (-18 - 9*2^(1+n) + 50*3^n + 9*4^n + 4*3^n*n) / 36.
(End)

A267467 Number of length-n 0..4 arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

5, 25, 115, 515, 2285, 10119, 44901, 200119, 897301, 4052183, 18444197, 84651063, 391805877, 1828676887, 8604122053, 40793238647, 194778656213, 936040595031, 4524410973669, 21981448319671, 107275320299509, 525571712299415

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Column 4 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = 19*a(n-1) -145*a(n-2) +565*a(n-3) -1174*a(n-4) +1216*a(n-5) -480*a(n-6).
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(5 - 70*x + 365*x^2 - 870*x^3 + 920*x^4 - 326*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2*(1 - 5*x)).
a(n) = (-80 - 15*2^(2+n) - 80*3^n + 335*4^n + 48*5^n) / 240 + 4^(-2+n)*n.
(End)

A267468 Number of length-n 0..5 arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

6, 36, 201, 1096, 5921, 31880, 171601, 925176, 5002641, 27155800, 148092161, 811801256, 4475004961, 24813260520, 138416411121, 776822970136, 4385905536881, 24907563562040, 142244725848481, 816667390335816

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Column 5 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = 26*a(n-1) -280*a(n-2) +1610*a(n-3) -5299*a(n-4) +9884*a(n-5) -9540*a(n-6) +3600*a(n-7).
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(6 - 120*x + 945*x^2 - 3710*x^3 + 7539*x^4 - 7336*x^5 + 2556*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)^2*(1 - 6*x)).
a(n) = (-75 - 25*2^(1+n) - 50*3^n + 25*2^(1+n)*3^n - 75*4^n + 413*5^n + 12*5^n*n) / 300.
(End)

A267469 Number of length-n 0..6 arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

7, 49, 322, 2072, 13216, 83972, 532840, 3381860, 21491464, 136856180, 873803848, 5596638788, 35973158152, 232118471828, 1503949949896, 9786663686756, 63969334316680, 420026972347316, 2770499256109384, 18356852895660164

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Column 6 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = 34*a(n-1) -490*a(n-2) +3892*a(n-3) -18529*a(n-4) +53746*a(n-5) -91860*a(n-6) +83448*a(n-7) -30240*a(n-8).
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(7 - 189*x + 2086*x^2 - 12110*x^3 + 39543*x^4 - 71617*x^5 + 65212*x^6 - 22212*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)^2*(1 - 7*x)).
a(n) = (-504 - 315*2^n - 280*3^n - 315*4^n - 504*5^n + 3409*6^n + 360*7^n + 35*2^(1+n)*3^n*n) / 2520.
(End)

A267470 Number of length-n 0..7 arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

8, 64, 484, 3592, 26440, 193852, 1418740, 10378144, 75944464, 556295860, 4080955516, 29994246136, 220942982968, 1631599880428, 12082194095812, 89736369169168, 668588308469152, 4997804102441956, 37486765952804428

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Column 7 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = 43*a(n-1) -798*a(n-2) +8358*a(n-3) -54201*a(n-4) +224427*a(n-5) -589112*a(n-6) +936452*a(n-7) -807408*a(n-8) +282240*a(n-9).
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: 4*x*(2 - 70*x + 1029*x^2 - 8253*x^3 + 39228*x^4 - 112119*x^5 + 185785*x^6 - 160106*x^7 + 53244*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)^2*(1 - 8*x)).
a(n) = (-980 - 147*2^(2+n) - 245*2^(1+2*n) - 490*3^n - 245*2^(2+n)*3^n - 588*5^n + 7818*7^n + 735*8^n + 120*7^n*n) / 5880.
(End)

A267472 Number of length-4 0..n arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

12, 62, 204, 515, 1096, 2072, 3592, 5829, 8980, 13266, 18932, 26247, 35504, 47020, 61136, 78217, 98652, 122854, 151260, 184331, 222552, 266432, 316504, 373325, 437476, 509562, 590212, 680079, 779840, 890196, 1011872, 1145617, 1292204

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Row 4 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = n^4 + (17/6)*n^3 + 4*n^2 + (19/6)*n + 1.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(12 + 2*x + 14*x^2 - 5*x^3 + 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)

A267473 Number of length-5 0..n arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

21, 160, 712, 2285, 5921, 13216, 26440, 48657, 83845, 137016, 214336, 323245, 472577, 672680, 935536, 1274881, 1706325, 2247472, 2918040, 3739981, 4737601, 5937680, 7369592, 9065425, 11060101, 13391496, 16100560, 19231437, 22831585

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Row 5 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = n^5 + (37/12)*n^4 + (11/2)*n^3 + (77/12)*n^2 + 4*n + 1.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(21 + 34*x + 67*x^2 - 7*x^3 + 6*x^4 - 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)

A267474 Number of length-6 0..n arrays with no following elements larger than the first repeated value.

Original entry on oeis.org

38, 418, 2490, 10119, 31880, 83972, 193852, 404589, 779938, 1410134, 2418406, 3968211, 6271188, 9595832, 14276888, 20725465, 29439870, 41017162, 56165426, 75716767, 100641024, 132060204, 171263636, 219723845, 279113146, 351320958

Offset: 1

R. H. Hardin, Jan 15 2016

nonn

Row 6 of A267471.

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

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

Cf. A267471.

Empirical: a(n) = n^6 + (197/60)*n^5 + 7*n^4 + (43/4)*n^3 + 10*n^2 + (149/30)*n + 1.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(38 + 152*x + 362*x^2 + 137*x^3 + 37*x^4 - 7*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

A267464 Number of length-n 0..n arrays with no following elements larger than the first repeated value.

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A267465 Number of length-n 0..2 arrays with no following elements larger than the first repeated value.

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A267466 Number of length-n 0..3 arrays with no following elements larger than the first repeated value.

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A267467 Number of length-n 0..4 arrays with no following elements larger than the first repeated value.

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A267468 Number of length-n 0..5 arrays with no following elements larger than the first repeated value.

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A267469 Number of length-n 0..6 arrays with no following elements larger than the first repeated value.

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A267470 Number of length-n 0..7 arrays with no following elements larger than the first repeated value.

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A267472 Number of length-4 0..n arrays with no following elements larger than the first repeated value.

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A267473 Number of length-5 0..n arrays with no following elements larger than the first repeated value.

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