A200886 -id:A200886 - cp's OEIS frontend

A200880 Number of 0..2 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

22, 51, 121, 292, 704, 1691, 4059, 9749, 23422, 56268, 135166, 324692, 779977, 1873673, 4500958, 10812237, 25973244, 62393157, 149881402, 360046432, 864906711, 2077686532, 4991036946, 11989513056, 28801314179, 69186771332

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 2 of A200886.

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

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

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5).

Empirical g.f.: x*(22 - 15*x + 34*x^2 - 6*x^3 + 9*x^4) / (1 - 3*x + 3*x^2 - 4*x^3 + x^4 - x^5). - Colin Barker, Oct 16 2017

A200881 Number of 0..3 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

Original entry on oeis.org

50, 144, 422, 1268, 3823, 11472, 34350, 102896, 308419, 924532, 2771101, 8305373, 24892609, 74608516, 223618304, 670231838, 2008825312, 6020872062, 18045827096, 54087163859, 162110668160, 485879938474, 1456284886944, 4364793695063

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 3 of A200886.

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

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

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7).

Empirical g.f.: x*(50 - 56*x + 146*x^2 - 56*x^3 + 93*x^4 - 12*x^5 + 16*x^6) / (1 - 4*x + 6*x^2 - 10*x^3 + 5*x^4 - 6*x^5 + x^6 - x^7). - Colin Barker, Oct 16 2017

A200882 Number of 0..4 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

Original entry on oeis.org

95, 325, 1121, 3985, 14288, 50995, 181336, 644721, 2294193, 8166441, 29066618, 103444256, 368138471, 1310164527, 4662787112, 16594519920, 59058487061, 210183969235, 748026706926, 2662163892493, 9474416502527, 33718645047381

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 4 of A200886.

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

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

Empirical: a(n) = 5*a(n-1) -10*a(n-2) +20*a(n-3) -15*a(n-4) +21*a(n-5) -7*a(n-6) +8*a(n-7) -a(n-8) +a(n-9).

Empirical g.f.: x*(95 - 150*x + 446*x^2 - 270*x^3 + 498*x^4 - 135*x^5 + 196*x^6 - 20*x^7 + 25*x^8) / (1 - 5*x + 10*x^2 - 20*x^3 + 15*x^4 - 21*x^5 + 7*x^6 - 8*x^7 + x^8 - x^9). - Colin Barker, Oct 16 2017

A200883 Number of 0..5 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

Original entry on oeis.org

161, 636, 2507, 10213, 42182, 173606, 710976, 2908797, 11911516, 48807427, 199987737, 819315100, 3356387171, 13749952752, 56330082115, 230771042950, 945410224602, 3873094298871, 15867039092263, 65003096433432

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 5 of A200886.

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

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

Empirical: a(n) = 6*a(n-1) -15*a(n-2) +35*a(n-3) -35*a(n-4) +56*a(n-5) -28*a(n-6) +36*a(n-7) -9*a(n-8) +10*a(n-9) -a(n-10) +a(n-11).

Empirical g.f.: x*(161 - 330*x + 1106*x^2 - 924*x^3 + 1884*x^4 - 792*x^5 + 1252*x^6 - 264*x^7 + 355*x^8 - 30*x^9 + 36*x^10) / (1 - 6*x + 15*x^2 - 35*x^3 + 35*x^4 - 56*x^5 + 28*x^6 - 36*x^7 + 9*x^8 - 10*x^9 + x^10 - x^11). - Colin Barker, Oct 16 2017

A200884 Number of 0..6 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

Original entry on oeis.org

252, 1127, 4977, 22736, 105813, 491533, 2269938, 10462235, 48259083, 222798408, 1028746629, 4749274209, 21922813539, 101196577809, 467142348798, 2156444661242, 9954648966159, 45952741121083, 212127214776309

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 6 of A200886.

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

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

Empirical: a(n) = 7*a(n-1) -21*a(n-2) +56*a(n-3) -70*a(n-4) +126*a(n-5) -84*a(n-6) +120*a(n-7) -45*a(n-8) +55*a(n-9) -11*a(n-10) +12*a(n-11) -a(n-12) +a(n-13).

Empirical g.f.: x*(252 - 637*x + 2380*x^2 - 2548*x^3 + 5706*x^4 - 3276*x^5 + 5620*x^6 - 1820*x^7 + 2630*x^8 - 455*x^9 + 582*x^10 - 42*x^11 + 49*x^12) / (1 - 7*x + 21*x^2 - 56*x^3 + 70*x^4 - 126*x^5 + 84*x^6 - 120*x^7 + 45*x^8 - 55*x^9 + 11*x^10 - 12*x^11 + x^12 - x^13). - Colin Barker, Oct 16 2017

A200885 Number of 0..7 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

Original entry on oeis.org

372, 1856, 9052, 45648, 235538, 1215616, 6233356, 31868448, 163014678, 834763824, 4276077566, 21900661172, 112149148911, 574278200480, 2940790043388, 15059692639376, 77120252989206, 394927990211792, 2022395235481866

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 7 of A200886.

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

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

Empirical: a(n) = 8*a(n-1) -28*a(n-2) +84*a(n-3) -126*a(n-4) +252*a(n-5) -210*a(n-6) +330*a(n-7) -165*a(n-8) +220*a(n-9) -66*a(n-10) +78*a(n-11) -13*a(n-12) +14*a(n-13) -a(n-14) +a(n-15).

Empirical g.f.: x*(372 - 1120*x + 4620*x^2 - 6048*x^3 + 14778*x^4 - 10800*x^5 + 20020*x^6 - 8800*x^7 + 13630*x^8 - 3600*x^9 + 4902*x^10 - 720*x^11 + 889*x^12 - 56*x^13 + 64*x^14) / (1 - 8*x + 28*x^2 - 84*x^3 + 126*x^4 - 252*x^5 + 210*x^6 - 330*x^7 + 165*x^8 - 220*x^9 + 66*x^10 - 78*x^11 + 13*x^12 - 14*x^13 + x^14 - x^15). - Colin Barker, Oct 16 2017

A200887 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors.

Original entry on oeis.org

12, 51, 144, 325, 636, 1127, 1856, 2889, 4300, 6171, 8592, 11661, 15484, 20175, 25856, 32657, 40716, 50179, 61200, 73941, 88572, 105271, 124224, 145625, 169676, 196587, 226576, 259869, 296700, 337311, 381952, 430881, 484364, 542675, 606096, 674917

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Row 2 of A200886.

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

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

Empirical: a(n) = (1/3)*n^4 + (7/3)*n^3 + (14/3)*n^2 + (11/3)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(12 - 9*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.
a(n) = (1+n)^2 * (3+5*n+n^2) / 3.
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)

A200888 Number of 0..n arrays x(0..4) of 5 elements without any interior element greater than both neighbors.

Original entry on oeis.org

21, 121, 422, 1121, 2507, 4977, 9052, 15393, 24817, 38313, 57058, 82433, 116039, 159713, 215544, 285889, 373389, 480985, 611934, 769825, 958595, 1182545, 1446356, 1755105, 2114281, 2529801, 3008026, 3555777, 4180351, 4889537, 5691632, 6595457

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Row 3 of A200886.

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

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

Empirical: a(n) = (2/15)*n^5 + (11/6)*n^4 + (35/6)*n^3 + (23/3)*n^2 + (68/15)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(21 - 5*x + 11*x^2 - 16*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)

A200889 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors.

Original entry on oeis.org

37, 292, 1268, 3985, 10213, 22736, 45648, 84681, 147565, 244420, 388180, 595049, 884989, 1282240, 1815872, 2520369, 3436245, 4610692, 6098260, 7961569, 10272053, 13110736, 16569040, 20749625, 25767261, 31749732, 38838772, 47191033, 56979085

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Row 4 of A200886.

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

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

Empirical: a(n) = (2/45)*n^6 + (19/15)*n^5 + (217/36)*n^4 + (71/6)*n^3 + (2057/180)*n^2 + (27/5)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(37 + 33*x + x^2 - 54*x^3 + 21*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)

A200890 Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors.

Original entry on oeis.org

65, 704, 3823, 14288, 42182, 105813, 235538, 478467, 904111, 1611038, 2734601, 4455802, 7011356, 10705019, 15920244, 23134229, 32933421, 46030540, 63283187, 85714100, 114533122, 151160945, 197254694, 254735415, 325817531, 413040330

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Row 5 of A200886.

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

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

Empirical: a(n) = (4/315)*n^7 + (7/9)*n^6 + (241/45)*n^5 + (1067/72)*n^4 + (3757/180)*n^3 + (1145/72)*n^2 + (2629/420)*n + 1.
Conjectures from Colin Barker, Oct 16 2017: (Start)
G.f.: x*(65 + 184*x + 11*x^2 - 224*x^3 + 48*x^4 - 27*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

A200880 Number of 0..2 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

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A200881 Number of 0..3 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

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A200882 Number of 0..4 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

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A200883 Number of 0..5 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

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A200884 Number of 0..6 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

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A200885 Number of 0..7 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.

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A200887 Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors.

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A200888 Number of 0..n arrays x(0..4) of 5 elements without any interior element greater than both neighbors.

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A200889 Number of 0..n arrays x(0..5) of 6 elements without any interior element greater than both neighbors.

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A200890 Number of 0..n arrays x(0..6) of 7 elements without any interior element greater than both neighbors.

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