A269435 -id:A269435 - cp's OEIS frontend

A269431 Number of length-n 0..4 arrays with no repeated value greater than the previous repeated value.

5, 25, 125, 615, 2995, 14455, 69235, 329430, 1558430, 7334806, 34364270, 160340610, 745362730, 3453222850, 15949215754, 73454841775, 337413819915, 1546145183895, 7068979186035, 32251365241137, 146853223312325, 667445619383425

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

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

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

Column 4 of A269435.

Empirical: a(n) = 20*a(n-1) - 155*a(n-2) + 560*a(n-3) - 810*a(n-4) - 136*a(n-5) + 810*a(n-6) + 560*a(n-7) + 155*a(n-8) + 20*a(n-9) + a(n-10).

Empirical g.f.: x*(5 - 75*x + 400*x^2 - 810*x^3 + 120*x^4 + 810*x^5 + 560*x^6 + 155*x^7 + 20*x^8 + x^9) / (1 - 4*x - x^2)^5. - Colin Barker, Jan 21 2019

A269432 Number of length-n 0..5 arrays with no repeated value greater than the previous repeated value.

Original entry on oeis.org

6, 36, 216, 1281, 7536, 44021, 255576, 1475871, 8482276, 48543777, 276756312, 1572394697, 8905537932, 50293202487, 283276001872, 1591658418642, 8922925364502, 49917266140917, 278703080519352, 1553227427718978

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

Column 5 of A269435.

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

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

Cf. A269435.

Empirical: a(n) = 30*a(n-1) -369*a(n-2) +2350*a(n-3) -7890*a(n-4) +11550*a(n-5) +895*a(n-6) -11550*a(n-7) -7890*a(n-8) -2350*a(n-9) -369*a(n-10) -30*a(n-11) -a(n-12)

A269433 Number of length-n 0..6 arrays with no repeated value greater than the previous repeated value.

Original entry on oeis.org

7, 49, 343, 2380, 16408, 112476, 767172, 5209554, 35236110, 237479970, 1595378190, 10686193980, 71386033740, 475694666700, 3162645548916, 20982275486907, 138930896958189, 918219765681883, 6058251819231325, 39906814296599320

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

Column 6 of A269435.

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

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

Cf. A269435.

Empirical: a(n) = 42*a(n-1) -749*a(n-2) +7308*a(n-3) -41601*a(n-4) +133686*a(n-5) -198037*a(n-6) -2136*a(n-7) +198037*a(n-8) +133686*a(n-9) +41601*a(n-10) +7308*a(n-11) +749*a(n-12) +42*a(n-13) +a(n-14)

A269434 Number of length-n 0..7 arrays with no repeated value greater than the previous repeated value.

Original entry on oeis.org

8, 64, 512, 4068, 32152, 252932, 1981512, 15465934, 120310016, 933059856, 7216323640, 55670133422, 428465939112, 3290601897928, 25221303496496, 192953793764769, 1473623863797808, 11236105478130612, 85542959337048488

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

Column 7 of A269435.

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

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

Cf. A269435.

Empirical: a(n) = 56*a(n-1) -1364*a(n-2) +18816*a(n-3) -159866*a(n-4) +846328*a(n-5) -2642416*a(n-6) +3954888*a(n-7) -157507*a(n-8) -3954888*a(n-9) -2642416*a(n-10) -846328*a(n-11) -159866*a(n-12) -18816*a(n-13) -1364*a(n-14) -56*a(n-15) -a(n-16)

A269436 Number of length-4 0..n arrays with no repeated value greater than the previous repeated value.

Original entry on oeis.org

15, 78, 250, 615, 1281, 2380, 4068, 6525, 9955, 14586, 20670, 28483, 38325, 50520, 65416, 83385, 104823, 130150, 159810, 194271, 234025, 279588, 331500, 390325, 456651, 531090, 614278, 706875, 809565, 923056, 1048080, 1185393, 1335775

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

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

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

Row 4 of A269435.

Empirical: a(n) = n^4 + 4*n^3 + (11/2)*n^2 + (7/2)*n + 1.
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: x*(15 + 3*x + 10*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)

A269437 Number of length-5 0..n arrays with no repeated value greater than the previous repeated value.

Original entry on oeis.org

28, 222, 964, 2995, 7536, 16408, 32152, 58149, 98740, 159346, 246588, 368407, 534184, 754860, 1043056, 1413193, 1881612, 2466694, 3188980, 4071291, 5138848, 6419392, 7943304, 9743725, 11856676, 14321178, 17179372, 20476639, 24261720

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

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

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

Row 5 of A269435.

Empirical: a(n) = n^5 + 5*n^4 + (17/2)*n^3 + 8*n^2 + (9/2)*n + 1.
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: x*(28 + 54*x + 52*x^2 - 19*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)

A269438 Number of length-6 0..n arrays with no repeated value greater than the previous repeated value.

Original entry on oeis.org

51, 622, 3674, 14455, 44021, 112476, 252932, 516189, 976135, 1735866, 2934526, 4754867, 7431529, 11260040, 16606536, 23918201, 33734427, 46698694, 63571170, 85242031, 112745501, 147274612, 190196684, 243069525, 307658351, 385953426

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

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

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

Row 6 of A269435.

Empirical: a(n) = n^6 + 6*n^5 + 12*n^4 + (44/3)*n^3 + (23/2)*n^2 + (29/6)*n + 1.
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: x*(51 + 265*x + 391*x^2 + 14*x^3 + 5*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)

A269439 Number of length-7 0..n arrays with no repeated value greater than the previous repeated value.

Original entry on oeis.org

92, 1722, 13868, 69235, 255576, 767172, 1981512, 4566213, 9621220, 18861326, 34844052, 61247927, 103206208, 167701080, 264023376, 404302857, 604114092, 883162978, 1266058940, 1783177851, 2471620712, 3376273132, 4550970648

Offset: 1

R. H. Hardin, Feb 26 2016

nonn

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

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

Row 7 of A269435.

Empirical: a(n) = n^7 + 7*n^6 + 16*n^5 + (71/3)*n^4 + (139/6)*n^3 + (43/3)*n^2 + (35/6)*n + 1.
Conjectures from Colin Barker, Jan 22 2019: (Start)
G.f.: x*(92 + 986*x + 2668*x^2 + 1355*x^3 + 8*x^4 - 76*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

cp's OEIS Frontend

A269431 Number of length-n 0..4 arrays with no repeated value greater than the previous repeated value.

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A269432 Number of length-n 0..5 arrays with no repeated value greater than the previous repeated value.

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A269433 Number of length-n 0..6 arrays with no repeated value greater than the previous repeated value.

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A269434 Number of length-n 0..7 arrays with no repeated value greater than the previous repeated value.

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A269436 Number of length-4 0..n arrays with no repeated value greater than the previous repeated value.

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A269437 Number of length-5 0..n arrays with no repeated value greater than the previous repeated value.

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A269438 Number of length-6 0..n arrays with no repeated value greater than the previous repeated value.

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A269439 Number of length-7 0..n arrays with no repeated value greater than the previous repeated value.

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