A269409 -id:A269409 - cp's OEIS frontend

A269405 Number of length-n 0..4 arrays with no repeated value greater than or equal to the previous repeated value.

5, 25, 120, 570, 2670, 12380, 56890, 259445, 1175355, 5293671, 23718780, 105781845, 469798125, 2078552055, 9164402118, 40277785365, 176503698495, 771372344695, 3362640467600, 14624384170213, 63463229049585, 274836205944615

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

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

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

Column 4 of A269409

Empirical: a(n) = 20*a(n-1) - 150*a(n-2) + 460*a(n-3) - 65*a(n-4) - 2472*a(n-5) + 2320*a(n-6) + 6400*a(n-7) - 3840*a(n-8) - 10240*a(n-9) - 4096*a(n-10).

Empirical g.f.: x*(5 - 75*x + 370*x^2 - 380*x^3 - 1905*x^4 + 3265*x^5 + 5590*x^6 - 5865*x^7 - 11455*x^8 - 4339*x^9) / ((1 + x)^4*(1 - 4*x)^6). - Colin Barker, Jan 21 2019

A269406 Number of length-n 0..5 arrays with no repeated value greater than or equal to the previous repeated value.

Original entry on oeis.org

6, 36, 210, 1215, 6960, 39560, 223320, 1253190, 6995660, 38870136, 215074596, 1185563746, 6512894520, 35666937840, 194765568024, 1060744346079, 5762980508994, 31239002042780, 168977143019910, 912220049428041

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

Column 5 of A269409.

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

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

Cf. A269409.

Empirical: a(n) = 30*a(n-1) -360*a(n-2) +2090*a(n-3) -4905*a(n-4) -5076*a(n-5) +41160*a(n-6) -9900*a(n-7) -151875*a(n-8) -6250*a(n-9) +300000*a(n-10) +281250*a(n-11) +78125*a(n-12)

A269407 Number of length-n 0..6 arrays with no repeated value greater than or equal to the previous repeated value.

Original entry on oeis.org

7, 49, 336, 2289, 15477, 104006, 695135, 4623815, 30625210, 202067047, 1328649469, 8708852838, 56920021347, 371043659463, 2412849114074, 15655214564192, 101363364976160, 655024985471255, 4225174990367555, 27207648363845138

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

Column 6 of A269409.

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

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

Cf. A269409.

Empirical: a(n) = 42*a(n-1) -735*a(n-2) +6748*a(n-3) -32319*a(n-4) +53130*a(n-5) +172655*a(n-6) -705840*a(n-7) -418320*a(n-8) +3386880*a(n-9) +2522016*a(n-10) -7402752*a(n-11) -13063680*a(n-12) -7838208*a(n-13) -1679616*a(n-14)

A269408 Number of length-n 0..7 arrays with no repeated value greater than or equal to the previous repeated value.

Original entry on oeis.org

8, 64, 504, 3948, 30744, 238224, 1837752, 14121282, 108123624, 825227424, 6279994728, 47663522844, 360868232424, 2726022470928, 20549497120776, 154606709405835, 1161096042133440, 8705061811230400, 65160664171875440

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

Column 7 of A269409.

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

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

Cf. A269409.

Empirical: a(n) = 56*a(n-1) -1344*a(n-2) +17752*a(n-3) -135716*a(n-4) +545496*a(n-5) -463792*a(n-6) -4675336*a(n-7) +12240018*a(n-8) +21847336*a(n-9) -72913568*a(n-10) -123833976*a(n-11) +152002508*a(n-12) +520479176*a(n-13) +513890832*a(n-14) +230592040*a(n-15) +40353607*a(n-16)

A269410 Number of length-4 0..n arrays with no repeated value greater than or equal to the previous repeated value.

Original entry on oeis.org

9, 63, 222, 570, 1215, 2289, 3948, 6372, 9765, 14355, 20394, 28158, 37947, 50085, 64920, 82824, 104193, 129447, 159030, 193410, 233079, 278553, 330372, 389100, 455325, 529659, 612738, 705222, 807795, 921165, 1046064, 1183248, 1333497

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

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

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

Row 4 of A269409.

Empirical: a(n) = n^4 + 4*n^3 + (7/2)*n^2 + (1/2)*n.
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: 3*x*(3 + 6*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)

A269411 Number of length-5 0..n arrays with no repeated value greater than or equal to the previous repeated value.

Original entry on oeis.org

12, 159, 804, 2670, 6960, 15477, 30744, 56124, 95940, 155595, 241692, 362154, 526344, 745185, 1031280, 1399032, 1864764, 2446839, 3165780, 4044390, 5107872, 6383949, 7902984, 9698100, 11805300, 14263587, 17115084, 20405154, 24182520

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

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

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

Row 5 of A269409.

Empirical: a(n) = n^5 + 5*n^4 + (11/2)*n^3 + n^2 - (1/2)*n.
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: 3*x*(4 + 29*x + 10*x^2 - 3*x^3) / (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)

A269412 Number of length-6 0..n arrays with no repeated value greater than or equal to the previous repeated value.

Original entry on oeis.org

16, 394, 2872, 12380, 39560, 104006, 238224, 492312, 939360, 1681570, 2857096, 4647604, 7286552, 11068190, 16357280, 23599536, 33332784, 46198842, 62956120, 84492940, 111841576, 146193014, 188912432, 241555400, 305884800, 383888466

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

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

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

Row 6 of A269409.

Empirical: a(n) = n^6 + 6*n^5 + 8*n^4 + (5/3)*n^3 - n^2 + (1/3)*n.
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: 2*x*(8 + 141*x + 225*x^2 - 5*x^3 - 9*x^4) / (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)

A269413 Number of length-7 0..n arrays with no repeated value greater than or equal to the previous repeated value.

Original entry on oeis.org

20, 957, 10132, 56890, 223320, 695135, 1837752, 4302612, 9168780, 18124865, 33696300, 59523022, 100692592, 164133795, 259075760, 397577640, 595133892, 871360197, 1250765060, 1763612130, 2446878280, 3345312487, 4512600552

Offset: 1

R. H. Hardin, Feb 25 2016

nonn

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

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

Row 7 of A269409.

Empirical: a(n) = n^7 + 7*n^6 + 11*n^5 + (8/3)*n^4 - (11/6)*n^3 + (1/3)*n^2 - (1/6)*n.
Conjectures from Colin Barker, Jan 21 2019: (Start)
G.f.: x*(20 + 797*x + 3036*x^2 + 1510*x^3 - 296*x^4 - 27*x^5) / (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

A269405 Number of length-n 0..4 arrays with no repeated value greater than or equal to the previous repeated value.

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A269406 Number of length-n 0..5 arrays with no repeated value greater than or equal to the previous repeated value.

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A269407 Number of length-n 0..6 arrays with no repeated value greater than or equal to the previous repeated value.

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A269408 Number of length-n 0..7 arrays with no repeated value greater than or equal to the previous repeated value.

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A269410 Number of length-4 0..n arrays with no repeated value greater than or equal to the previous repeated value.

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A269411 Number of length-5 0..n arrays with no repeated value greater than or equal to the previous repeated value.

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A269412 Number of length-6 0..n arrays with no repeated value greater than or equal to the previous repeated value.

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A269413 Number of length-7 0..n arrays with no repeated value greater than or equal to the previous repeated value.

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