A250361 -id:A250361 - cp's OEIS frontend

A250357 Number of length n arrays x(i), i=1..n with x(i) in i..i+4 and no value appearing more than 3 times.

5, 25, 125, 623, 3094, 15365, 76300, 378880, 1881364, 9342081, 46388915, 230348138, 1143813376, 5679703079, 28203050974, 140044659409, 695403722139, 3453086599482, 17146596550508, 85142890221146, 422784296221329

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

			Some solutions for n=6:
..2....4....0....0....2....2....0....2....0....1....3....3....4....1....2....0
..4....3....4....2....2....3....2....3....4....1....2....1....4....1....5....3
..2....5....5....5....6....6....4....6....3....2....2....5....5....5....6....6
..4....6....7....6....3....5....5....4....7....4....4....7....4....4....7....3
..8....7....4....5....5....8....6....4....7....7....5....6....6....8....6....8
..7....9....9....6....5....7....7....8....6....5....5....7....6....5....8....9

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

Column 4 of A250361.

Empirical: a(n) = 5*a(n-1) - 2*a(n-4) - 11*a(n-5) + a(n-8).

Empirical g.f.: x*(5 - 2*x^3 - 11*x^4 + x^7) / (1 - 5*x + 2*x^4 + 11*x^5 - x^8). - Colin Barker, Nov 13 2018

A250358 Number of length n arrays x(i), i=1..n with x(i) in i..i+5 and no value appearing more than 3 times.

Original entry on oeis.org

6, 36, 216, 1293, 7712, 45866, 272760, 1621963, 9644496, 57346376, 340979312, 2027446948, 12055094608, 71678940042, 426199029864, 2534155836542, 15067950109140, 89593195408640, 532716168060704, 3167500770096043

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

Column 5 of A250361

			Some solutions for n=6
..4....5....2....0....1....1....3....0....1....4....2....0....2....3....1....3
..1....2....6....1....6....5....2....2....6....4....2....1....4....1....2....1
..7....6....5....7....6....6....4....7....4....7....2....7....3....7....3....2
..6....6....4....8....6....8....8....4....6....6....8....7....3....4....7....6
..4....6....5....4....9....7....8....8....4....5....9....9....6....4....6....7
.10....8....9....6....5....6....8....6...10....7....8....5....9....8....7....7

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

Empirical: a(n) = 6*a(n-1) -4*a(n-4) -22*a(n-5) -130*a(n-6) +7*a(n-8) +50*a(n-9) +66*a(n-10) +a(n-12) -6*a(n-13)

A250359 Number of length n arrays x(i), i=1..n with x(i) in i..i+6 and no value appearing more than 3 times.

Original entry on oeis.org

7, 49, 343, 2397, 16700, 115963, 803382, 5565230, 38548644, 266998350, 1849229664, 12807494729, 88702171850, 614332682800, 4254735401463, 29467361754942, 204084413284570, 1413443236278923, 9789192962198232, 67797768520165387

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

Column 6 of A250361

			Some solutions for n=6
..1....3....5....1....1....1....1....0....4....1....2....4....5....3....2....2
..1....4....2....2....6....7....3....6....7....7....1....6....6....6....5....1
..7....8....7....7....4....3....2....6....3....4....8....8....8....7....7....5
..4....3....4....7....3....5....6....8....8....4....4....7....6....3....4....7
..7....7....7....6....9....7....7....5...10....4....4....4....7....9....5...10
..7....9....5....6....6....8....6....7....8....6....7....5....9....6....7....8

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

Empirical: a(n) = 7*a(n-1) -8*a(n-4) -40*a(n-5) -265*a(n-6) -1800*a(n-7) +38*a(n-8) +336*a(n-9) +1937*a(n-10) +3833*a(n-11) +6318*a(n-12) +303*a(n-13) -1245*a(n-14) -3056*a(n-15) -1258*a(n-16) +725*a(n-17) +1024*a(n-18) +343*a(n-19) +34*a(n-20) -137*a(n-21) -77*a(n-22) +47*a(n-24) +14*a(n-25)

A250360 Number of length n arrays x(i), i=1..n with x(i) in i..i+7 and no value appearing more than 3 times.

Original entry on oeis.org

8, 64, 512, 4091, 32608, 259106, 2052904, 16234706, 128373416, 1015004124, 8024737888, 63441430784, 501536079048, 3964832287906, 31343315384096, 247778886499164, 1958768810680376, 15484663643904612, 122410935014171288

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

Column 7 of A250361

			Some solutions for n=5
..7....4....3....7....1....7....4....4....3....7....4....5....6....7....1....0
..7....1....8....5....6....3....2....1....2....1....8....3....5....5....2....5
..6....7....9....3....7....3....3....4....6....4....7....3....7....6....6....8
..5...10....7...10...10....4....6....7....6....6....6....5....9....8....3....5
.11....8....8....4....7....6....7....9....6....8....4...11...11...11....5...10

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

Empirical: a(n) = 8*a(n-1) -16*a(n-4) -64*a(n-5) -488*a(n-6) -3752*a(n-7) -29038*a(n-8) +1592*a(n-9) +11770*a(n-10) +66616*a(n-11) +151100*a(n-12) +472248*a(n-13) +953904*a(n-14) +183480*a(n-15) -568091*a(n-16) -1229632*a(n-17) -708460*a(n-18) -48256*a(n-19) +682669*a(n-20) -62120*a(n-21) +527060*a(n-22) +1075872*a(n-23) +1391771*a(n-24) +726760*a(n-25) +633398*a(n-26) +879696*a(n-27) +723511*a(n-28) -757912*a(n-29) -103140*a(n-30) +79256*a(n-31) +602486*a(n-32) -304224*a(n-33) -111134*a(n-34) -350584*a(n-35) +418679*a(n-36) -76624*a(n-37) +104514*a(n-38) -256568*a(n-39) +138277*a(n-40) -37600*a(n-41) +136030*a(n-42) -105232*a(n-43) +18365*a(n-44) -15688*a(n-45) +34876*a(n-46) -16992*a(n-47) -905*a(n-48) -4336*a(n-49) -24*a(n-50) -1968*a(n-52) -192*a(n-53) +12*a(n-56)

A250362 Number of length 4 arrays x(i), i=1..4 with x(i) in i..i+n and no value appearing more than 3 times.

Original entry on oeis.org

16, 81, 255, 623, 1293, 2397, 4091, 6555, 9993, 14633, 20727, 28551, 38405, 50613, 65523, 83507, 104961, 130305, 159983, 194463, 234237, 279821, 331755, 390603, 456953, 531417, 614631, 707255, 809973, 923493, 1048547, 1185891, 1336305

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

			Some solutions for n=6:
..1....2....1....3....1....5....3....5....0....0....5....0....5....3....2....4
..2....3....5....7....4....6....4....3....3....2....6....5....4....4....4....6
..8....4....2....5....2....8....7....2....6....5....4....7....6....7....3....2
..3....6....6....9....9....6....7....4....8....7....5....6....7....9....4....9

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

Row 4 of A250361.

Empirical: a(n) = n^4 + 4*n^3 + 6*n^2 + 3*n + 3 for n>1.
Conjectures from Colin Barker, Nov 13 2018: (Start)
G.f.: x*(16 + x + 10*x^2 - 2*x^3 - 2*x^4 + x^5) / (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>6.
(End)

A250363 Number of length 5 arrays x(i), i=1..5 with x(i) in i..i+n and no value appearing more than 3 times.

Original entry on oeis.org

32, 243, 1016, 3094, 7712, 16700, 32608, 58826, 99704, 160672, 248360, 370718, 537136, 758564, 1047632, 1418770, 1888328, 2474696, 3198424, 4082342, 5151680, 6434188, 7960256, 9763034, 11878552, 14345840, 17207048, 20507566, 24296144

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

			Some solutions for n=6:
..1....2....1....2....5....3....5....4....4....3....3....6....2....2....1....3
..3....2....7....4....6....5....5....3....1....1....5....2....7....5....1....7
..6....2....6....5....8....2....4....3....5....7....6....5....8....6....3....4
..4....3....4....8....8....5....6....9....7....4....6....8....4....5....9....9
..4....7....9....4...10...10...10....9....4...10....4...10....9....4...10...10

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

Row 5 of A250361.

Empirical: a(n) = n^5 + 5*n^4 + 10*n^3 + 5*n^2 + 17*n + 2 for n>2.
Conjectures from Colin Barker, Nov 13 2018: (Start)
G.f.: x*(32 + 51*x + 38*x^2 + 3*x^3 + 8*x^4 - 29*x^5 + 22*x^6 - 5*x^7) / (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>8.
(End)

A250364 Number of length 6 arrays x(i), i=1..6 with x(i) in i..i+n and no value appearing more than 3 times.

Original entry on oeis.org

64, 729, 4048, 15365, 45866, 115963, 259106, 526505, 992530, 1760831, 2971178, 4807021, 7503770, 11357795, 16736146, 24086993, 33950786, 46972135, 63912410, 85663061, 113259658, 147896651, 190942850, 243957625, 308707826, 387185423

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

			Some solutions for n=6:
..2....1....5....4....5....4....1....0....0....1....5....4....5....5....0....4
..2....6....4....7....2....6....4....1....1....5....5....4....1....3....4....4
..3....8....6....7....2....7....6....3....7....4....8....8....6....2....7....7
..8....7....4....5....7....7....8....5....5....4....8....8....8....9....9....7
..8....7....4....5....4....7....4....9....8....8....4....9....6....8....4....8
..7...11....7...10....7....8....8....6....5....6...10....7....9....6....7....8

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

Row 6 of A250361.

Empirical: a(n) = n^6 + 6*n^5 + 15*n^4 + 5*n^3 + 57*n^2 + 13*n + 1 for n>3.
Conjectures from Colin Barker, Nov 13 2018: (Start)
G.f.: x*(64 + 281*x + 289*x^2 + 98*x^3 + 44*x^4 + 57*x^5 - 405*x^6 + 482*x^7 - 232*x^8 + 42*x^9) / (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>10.
(End)

A250365 Number of length 7 arrays x(i), i=1..7 with x(i) in i..i+n and no value appearing more than 3 times.

Original entry on oeis.org

128, 2187, 16128, 76300, 272760, 803382, 2052904, 4698744, 9854280, 19251970, 35471832, 62220324, 104664664, 169827630, 267047880, 408510832, 609855144, 890859834, 1276217080, 1796395740, 2488600632, 3397832614, 4578054504

Offset: 1

R. H. Hardin, Nov 19 2014

nonn

Row 7 of A250361

			Some solutions for n=4
..4....3....2....2....1....2....1....0....2....3....3....1....0....1....4....4
..4....5....4....2....5....2....1....2....5....1....2....2....5....2....4....5
..3....3....6....4....6....2....2....5....4....2....2....6....6....3....4....4
..5....7....6....5....3....4....7....3....6....6....6....6....7....6....3....7
..4....8....4....5....5....8....7....5....4....8....7....8....4....8....5....6
..6....7....5....7....5....6....9....8....9....8....9....7....5....9....9....5
..6....7....7....7....7....9....9....8....8...10....6...10...10....7....8....8

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

Empirical: a(n) = n^7 + 7*n^6 + 21*n^5 + 147*n^3 + 49*n^2 + 7*n for n>4

cp's OEIS Frontend

A250357 Number of length n arrays x(i), i=1..n with x(i) in i..i+4 and no value appearing more than 3 times.

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A250358 Number of length n arrays x(i), i=1..n with x(i) in i..i+5 and no value appearing more than 3 times.

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A250359 Number of length n arrays x(i), i=1..n with x(i) in i..i+6 and no value appearing more than 3 times.

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A250360 Number of length n arrays x(i), i=1..n with x(i) in i..i+7 and no value appearing more than 3 times.

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A250362 Number of length 4 arrays x(i), i=1..4 with x(i) in i..i+n and no value appearing more than 3 times.

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A250363 Number of length 5 arrays x(i), i=1..5 with x(i) in i..i+n and no value appearing more than 3 times.

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A250364 Number of length 6 arrays x(i), i=1..6 with x(i) in i..i+n and no value appearing more than 3 times.

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A250365 Number of length 7 arrays x(i), i=1..7 with x(i) in i..i+n and no value appearing more than 3 times.

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