A217964 -id:A217964 - cp's OEIS frontend

A217958 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 n X 2 array.

3, 17, 77, 343, 1523, 6761, 30013, 133231, 591427, 2625409, 11654477, 51735495, 229659507, 1019483609, 4525598973, 20089627615, 89180048899, 395879967217, 1757354367693, 7801087777591, 34629879796851, 153725814775369

Offset: 1

R. H. Hardin, Oct 16 2012

nonn

Column 2 of A217964.

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

R. H. Hardin, Table of n, a(n) for n = 1..179

Cf. A217964.

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

Empirical g.f.: x*(1 + x)*(3 + 2*x + x^2) / (1 - 4*x - 2*x^2 + x^4). - Colin Barker, Jul 23 2018

A217959 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 n X 3 array.

Original entry on oeis.org

9, 91, 835, 7765, 72257, 672627, 6261827, 58295677, 542717361, 5052561371, 47038082435, 437912812805, 4076859114817, 37954542163107, 353347327405987, 3289575547592237, 30625128435267441, 285112312553286091

Offset: 1

R. H. Hardin, Oct 16 2012

nonn

Column 3 of A217964.

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

R. H. Hardin, Table of n, a(n) for n = 1..181

Cf. A217964.

Empirical: a(n) = 10*a(n-1) - 4*a(n-2) - 20*a(n-3) - 23*a(n-4) - 10*a(n-5).

Empirical g.f.: x*(9 + x - 39*x^2 - 41*x^3 - 26*x^4) / (1 - 10*x + 4*x^2 + 20*x^3 + 23*x^4 + 10*x^5). - Colin Barker, Jul 23 2018

A217960 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX4 array.

Original entry on oeis.org

17, 321, 5415, 93765, 1602741, 27317977, 465184959, 7919256577, 134805742899, 2294680520773, 39060078023831, 664879775228995, 11317562137329901, 192647146079979077, 3279232808653682467, 55818982418231563527

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Column 4 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..38

Empirical: a(n) = 19*a(n-1) -23*a(n-2) -144*a(n-3) -675*a(n-4) +378*a(n-5) +3291*a(n-6) +4937*a(n-7) -1247*a(n-8) -12054*a(n-9) -12369*a(n-10) -5436*a(n-11) -816*a(n-12) +744*a(n-13) +364*a(n-14) +100*a(n-15) for n>16

A217961 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX5 array.

Original entry on oeis.org

37, 1341, 45043, 1483419, 48942485, 1616011915, 53384245121, 1763824455789, 58280433586547, 1925743948194651, 63632217591257991, 2102599141468586591, 69476223859440531703, 2295704722842360530889, 75857038242320718831657

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Column 5 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..20

A217962 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX6 array.

Original entry on oeis.org

77, 5269, 336927, 21409033, 1368783313, 87208470529, 5551631519475, 353274013599547, 22477653727743707, 1430126177007282011, 90989884584417998497, 5789093378881065959333, 368321970039635438136601

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Column 6 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..14

A217963 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX7 array.

Original entry on oeis.org

163, 21379, 2675127, 325878175, 40300213599, 4947545467377, 607719550822787, 74647005556631863, 9169731186564334011, 1126450063274952572801, 138379453182179987226615, 16999363267022602878612943

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Column 7 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..13

A217965 Number of 2Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 2Xn array.

Original entry on oeis.org

9, 17, 91, 321, 1341, 5269, 21379, 85633, 344955, 1386679, 5579199, 22440525, 90271591, 363117835, 1460674773, 5875648527, 23635221447, 95074256043, 382442764281, 1538402105163, 6188327969265, 24892972759953, 100133687989929

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Row 2 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..129

Empirical: a(n) = 2*a(n-1) +7*a(n-2) +6*a(n-3) -2*a(n-4) -10*a(n-5) -11*a(n-6) -32*a(n-7) -23*a(n-8) -16*a(n-9) +22*a(n-10) +4*a(n-11)

A217966 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 3Xn array.

Original entry on oeis.org

27, 77, 835, 5415, 45043, 336927, 2675127, 20711527, 162237197, 1264467637, 9878676929, 77096409709, 601984698319, 4699383563019, 36689365591653, 286431238079077, 2236192425051273, 17457988805711127, 136295317877977821

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Row 3 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..32

A217967 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 4Xn array.

Original entry on oeis.org

81, 343, 7765, 93765, 1483419, 21409033, 325878175, 4873250877, 73450141827, 1104008971493, 16615223109133, 249949206695547, 3760847564430971, 56583449950921439, 851347218771176575, 12809113773490102743

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Row 4 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..21

A217968 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 5Xn array.

Original entry on oeis.org

243, 1523, 72257, 1602741, 48942485, 1368783313, 40300213599, 1170265289539, 34202123230555, 997730409895429, 29128167430767449, 850254151548959837, 24820794901995097417, 724574515854245379961, 21151965211624408172993

Offset: 1

R. H. Hardin Oct 16 2012

nonn

Row 5 of A217964

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

R. H. Hardin, Table of n, a(n) for n = 1..24

cp's OEIS Frontend

A217958 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 n X 2 array.

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A217959 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 n X 3 array.

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A217960 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX4 array.

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A217961 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX5 array.

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A217962 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX6 array.

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A217963 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 nX7 array.

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A217965 Number of 2Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 2Xn array.

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A217966 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 3Xn array.

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A217967 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 4Xn array.

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A217968 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 5Xn array.

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