A229012 -id:A229012 - cp's OEIS frontend

A229013 Number of arrays of median of three adjacent elements of some length-5 0..n array, with no adjacent equal elements in the latter.

2, 15, 46, 101, 186, 307, 470, 681, 946, 1271, 1662, 2125, 2666, 3291, 4006, 4817, 5730, 6751, 7886, 9141, 10522, 12035, 13686, 15481, 17426, 19527, 21790, 24221, 26826, 29611, 32582, 35745, 39106, 42671, 46446, 50437, 54650, 59091, 63766, 68681, 73842

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

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

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

Row 3 of A229012.

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

A229006 Number of arrays of median of three adjacent elements of some length n+2 0..2 array, with no adjacent equal elements in the latter.

Original entry on oeis.org

3, 7, 15, 31, 57, 105, 193, 353, 653, 1209, 2241, 4161, 7719, 14325, 26581, 49311, 91489, 169729, 314881, 584177, 1083761, 2010609, 3730105, 6920121, 12838307, 23817773, 44187025, 81976335, 152083481, 282147169, 523442893, 971097649

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

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

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

Column 2 of A229012.

Empirical: a(n) = 2*a(n-1) - a(n-3) + 2*a(n-5) - a(n-6) + 2*a(n-8) - a(n-9) + 2*a(n-11) - 2*a(n-12) + 2*a(n-13).

Empirical g.f.: x*(3 + x + x^2 + 4*x^3 + 2*x^4 + 3*x^6 + x^7 - x^8 + 2*x^9 - 2*x^11 + 2*x^12) / (1 - 2*x + x^3 - 2*x^5 + x^6 - 2*x^8 + x^9 - 2*x^11 + 2*x^12 - 2*x^13). - Colin Barker, Sep 13 2018

A229007 Number of arrays of median of three adjacent elements of some length n+2 0..3 array, with no adjacent equal elements in the latter.

Original entry on oeis.org

4, 14, 46, 130, 332, 830, 2054, 5108, 12790, 32146, 80942, 203898, 513498, 1292934, 3254868, 8193210, 20623908, 51914372, 130680214, 328953874, 828059138, 2084434524, 5247046924, 13208134738, 33248182980, 83693989466, 210678694852

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

Column 3 of A229012.

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

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

Empirical: a(n) = 3*a(n-1) -5*a(n-3) +2*a(n-4) +11*a(n-5) -11*a(n-6) -2*a(n-7) +19*a(n-8) -8*a(n-9) -13*a(n-10) +28*a(n-11) -18*a(n-12) +a(n-13) +26*a(n-14) -24*a(n-15) +9*a(n-16) +15*a(n-17) -21*a(n-18) +13*a(n-19) +5*a(n-20) -12*a(n-21) +19*a(n-22) -9*a(n-23) -a(n-24) +4*a(n-25) -4*a(n-26) +2*a(n-27).

A229008 Number of arrays of median of three adjacent elements of some length n+2 0..4 array, with no adjacent equal elements in the latter.

Original entry on oeis.org

5, 23, 101, 359, 1145, 3527, 10735, 32907, 101635, 315579, 982305, 3059025, 9524031, 29640801, 92224095, 286910991, 892560177, 2776725201, 8638459639, 26874806287, 83609764417, 260117322353, 809247413805, 2517636208515, 7832571212121

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

Column 4 of A229012.

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

R. H. Hardin, Table of n, a(n) for n = 1..136

Empirical: a(n) = 4*a(n-1) -a(n-2) -10*a(n-3) +7*a(n-4) +35*a(n-5) -47*a(n-6) -9*a(n-7) +106*a(n-8) -43*a(n-9) -123*a(n-10) +248*a(n-11) -30*a(n-12) -255*a(n-13) +370*a(n-14) +13*a(n-15) -396*a(n-16) +484*a(n-17) +88*a(n-18) -609*a(n-19) +715*a(n-20) -62*a(n-21) -603*a(n-22) +830*a(n-23) -305*a(n-24) -450*a(n-25) +825*a(n-26) -580*a(n-27) -91*a(n-28) +586*a(n-29) -678*a(n-30) +304*a(n-31) +130*a(n-32) -423*a(n-33) +364*a(n-34) -103*a(n-35) -83*a(n-36) +176*a(n-37) -111*a(n-38) +25*a(n-39) +37*a(n-40) -32*a(n-41) +17*a(n-42) -2*a(n-43) -4*a(n-44) +2*a(n-45) -a(n-46).

A229009 Number of arrays of median of three adjacent elements of some length n+2 0..5 array, with no adjacent equal elements in the latter.

Original entry on oeis.org

6, 34, 186, 794, 3002, 10860, 38768, 139456, 506236, 1849846, 6780968, 24874236, 91221120, 334365156, 1225151856, 4488311694, 16442040398, 60232977210, 220660283800, 808393136582, 2961592442222, 10849984832400, 39749595896184

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

Column 5 of A229012.

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

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

Empirical: a(n) = 5*a(n-1) -2*a(n-2) -20*a(n-3) +22*a(n-4) +82*a(n-5) -149*a(n-6) -43*a(n-7) +448*a(n-8) -234*a(n-9) -682*a(n-10) +1345*a(n-11) +224*a(n-12) -2593*a(n-13) +2526*a(n-14) +1704*a(n-15) -5131*a(n-16) +3300*a(n-17) +3626*a(n-18) -8749*a(n-19) +6357*a(n-20) +4147*a(n-21) -16222*a(n-22) +17531*a(n-23) -1049*a(n-24) -26481*a(n-25) +39209*a(n-26) -20438*a(n-27) -26566*a(n-28) +64130*a(n-29) -57341*a(n-30) +140*a(n-31) +70204*a(n-32) -97044*a(n-33) +51459*a(n-34) +41116*a(n-35) -107708*a(n-36) +100930*a(n-37) -16302*a(n-38) -75708*a(n-39) +115023*a(n-40) -67934*a(n-41) -19000*a(n-42) +85062*a(n-43) -80464*a(n-44) +25613*a(n-45) +34418*a(n-46) -57825*a(n-47) +36505*a(n-48) +585*a(n-49) -24392*a(n-50) +24406*a(n-51) -9363*a(n-52) -5285*a(n-53) +9392*a(n-54) -6018*a(n-55) +851*a(n-56) +2156*a(n-57) -2078*a(n-58) +767*a(n-59) +139*a(n-60) -384*a(n-61) +244*a(n-62) -37*a(n-63) -36*a(n-64) +32*a(n-65) -11*a(n-66) +2*a(n-68) -a(n-69)

A229010 Number of arrays of median of three adjacent elements of some length n+2 0..6 array, with no adjacent equal elements in the latter.

Original entry on oeis.org

7, 47, 307, 1527, 6635, 27379, 111311, 456029, 1888383, 7880975, 33018001, 138469191, 580547651, 2432537637, 10187801775, 42657765711, 178601463643, 747785468741, 3131002111003, 13109964303805, 54894127263817

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

Column 6 of A229012.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 95

Empirical recurrence of order 95 (see link above).

A229011 Number of arrays of median of three adjacent elements of some length n+2 0..7 array, with no adjacent equal elements in the latter.

Original entry on oeis.org

8, 62, 470, 2666, 13040, 60180, 273124, 1248872, 5780144, 26993340, 126638342, 594901860, 2793932346, 13112533536, 61505348386, 288407464930, 1352248997558, 6340299132898, 29728967922162, 139400729229576, 653670375108782

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

Column 7 of A229012.

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

R. H. Hardin, Table of n, a(n) for n = 1..127

A229014 Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter.

Original entry on oeis.org

2, 31, 130, 359, 794, 1527, 2666, 4335, 6674, 9839, 14002, 19351, 26090, 34439, 44634, 56927, 71586, 88895, 109154, 132679, 159802, 190871, 226250, 266319, 311474, 362127, 418706, 481655, 551434, 628519, 713402, 806591, 908610, 1019999, 1141314

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

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

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

Row 4 of A229012.

Empirical: a(n) = (2/3)*n^4 + (10/3)*n^3 - (5/3)*n^2 + (2/3)*n - 1.
Conjectures from Colin Barker, Sep 13 2018: (Start)
G.f.: x*(2 - x)*(1 + 11*x + 3*x^2 + x^3) / (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)

A229015 Number of arrays of median of three adjacent elements of some length 7 0..n array, with no adjacent equal elements in the latter.

Original entry on oeis.org

2, 57, 332, 1145, 3002, 6635, 13040, 23515, 39698, 63605, 97668, 144773, 208298, 292151, 400808, 539351, 713506, 929681, 1195004, 1517361, 1905434, 2368739, 2917664, 3563507, 4318514, 5195917, 6209972, 7375997, 8710410, 10230767

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

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

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

Row 5 of A229012.

Empirical: a(n) = (19/60)*n^5 + (37/12)*n^4 + (19/12)*n^3 - (61/12)*n^2 + (31/10)*n - 1.
Conjectures from Colin Barker, Sep 13 2018: (Start)
G.f.: x*(2 + 45*x + 20*x^2 - 32*x^3 + 2*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)

A229016 Number of arrays of median of three adjacent elements of some length 8 0..n array, with no adjacent equal elements in the latter.

Original entry on oeis.org

2, 105, 830, 3527, 10860, 27379, 60180, 119653, 220318, 381749, 629586, 996635, 1524056, 2262639, 3274168, 4632873, 6426970, 8760289, 11753990, 15548367, 20304740, 26207435, 33465852, 42316621, 53025846, 65891437, 81245530, 99456995

Offset: 1

R. H. Hardin, Sep 10 2013

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..178

Row 6 of A229012.

Empirical: a(n) = (11/90)*n^6 + (11/5)*n^5 + (167/36)*n^4 - (43/6)*n^3 + (583/180)*n^2 - (61/30)*n + 1.
Conjectures from Colin Barker, Sep 14 2018: (Start)
G.f.: x*(2 + 91*x + 137*x^2 - 148*x^3 - 4*x^4 + 9*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

A229013 Number of arrays of median of three adjacent elements of some length-5 0..n array, with no adjacent equal elements in the latter.

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A229006 Number of arrays of median of three adjacent elements of some length n+2 0..2 array, with no adjacent equal elements in the latter.

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A229007 Number of arrays of median of three adjacent elements of some length n+2 0..3 array, with no adjacent equal elements in the latter.

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A229008 Number of arrays of median of three adjacent elements of some length n+2 0..4 array, with no adjacent equal elements in the latter.

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A229009 Number of arrays of median of three adjacent elements of some length n+2 0..5 array, with no adjacent equal elements in the latter.

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A229010 Number of arrays of median of three adjacent elements of some length n+2 0..6 array, with no adjacent equal elements in the latter.

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A229011 Number of arrays of median of three adjacent elements of some length n+2 0..7 array, with no adjacent equal elements in the latter.

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A229014 Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter.

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A229015 Number of arrays of median of three adjacent elements of some length 7 0..n array, with no adjacent equal elements in the latter.

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A229016 Number of arrays of median of three adjacent elements of some length 8 0..n array, with no adjacent equal elements in the latter.

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