A218522 -id:A218522 - cp's OEIS frontend

A218516 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 n X 2 array.

4, 36, 236, 1528, 9858, 63592, 410218, 2646208, 17069998, 110114102, 710317326, 4582071648, 29557748082, 190669317026, 1229957991200, 7934137929012, 51181052626992, 330155610028966, 2129747655406998, 13738446168804038

Offset: 1

R. H. Hardin, Oct 31 2012

nonn

Column 2 of A218522.

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

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

Cf. A218522.

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

Empirical g.f.: 2*x*(2 + 6*x + 4*x^2 + 2*x^3 - x^4) / (1 - 6*x - 3*x^2 + 4*x^4 - x^5). - Colin Barker, Jul 24 2018

A218517 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 n X 3 array.

Original entry on oeis.org

16, 286, 4634, 76214, 1254462, 20655650, 340133516, 5601018048, 92232936766, 1518816980614, 25010647012824, 411855079591306, 6782095959978908, 111682064830460636, 1839089815861812230, 30284641999299892776

Offset: 1

R. H. Hardin, Oct 31 2012

nonn

Column 3 of A218522.

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

R. H. Hardin, Table of n, a(n) for n = 1..157

Cf. A218522.

Empirical: a(n) = 18*a(n-1) - 19*a(n-2) - 96*a(n-3) - 112*a(n-4) - a(n-5) + 140*a(n-6) + 64*a(n-7).

Empirical g.f.: 2*x*(8 - x - 105*x^2 - 114*x^3 - 48*x^4 + 156*x^5 + 96*x^6) / (1 - 18*x + 19*x^2 + 96*x^3 + 112*x^4 + x^5 - 140*x^6 - 64*x^7). - Colin Barker, Jul 24 2018

A218518 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX4 array.

Original entry on oeis.org

36, 1348, 46140, 1608968, 55161270, 1884162624, 64278999490, 2192134613268, 74751612059942, 2548947544959236, 86915544096055764, 2963690927218083408, 101057383442299027280, 3445903376402787417912, 117500067196994800465952

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Column 4 of A218522

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

R. H. Hardin, Table of n, a(n) for n = 1..61

Empirical: a(n) = 42*a(n-1) -245*a(n-2) -717*a(n-3) -5326*a(n-4) +43148*a(n-5) +128181*a(n-6) -176404*a(n-7) -1716466*a(n-8) -2364600*a(n-9) +12012574*a(n-10) +11501431*a(n-11) -58267109*a(n-12) -51447755*a(n-13) +49462902*a(n-14) +161410534*a(n-15) +79479210*a(n-16) -105405324*a(n-17) -153176469*a(n-18) -54313004*a(n-19) +39086790*a(n-20) +45585629*a(n-21) +16699655*a(n-22) +1770396*a(n-23) -935268*a(n-24) -336384*a(n-25) -57600*a(n-26) for n>27

A218519 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX5 array.

Original entry on oeis.org

94, 7902, 639228, 49466988, 3856183182, 300890728324, 23498366579584, 1835588124922808, 143401026618956100, 11203192491897097878, 875256805363669114070, 68380229008811109398218, 5342272688474066298382144

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Column 5 of A218522

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

R. H. Hardin, Table of n, a(n) for n = 1..42

A218520 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX6 array.

Original entry on oeis.org

236, 42812, 7687526, 1326731972, 232640291710, 40522780697742, 7051080210074740, 1226141540661411646, 213181725321313805184, 37062512930409971808074, 6443364732821356673971218

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Column 6 of A218522

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

R. H. Hardin, Table of n, a(n) for n = 1..67

A218521 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX7 array.

Original entry on oeis.org

602, 242438, 100029148, 38497164700, 15254005086276, 5977895789290552, 2345237392530015812, 920135128267216305816, 361061212834288178529464, 141687156380002483076174644, 55601697647561060078651796422

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Column 7 of A218522

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

R. H. Hardin, Table of n, a(n) for n = 1..53

A218523 Number of 2Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 2Xn array.

Original entry on oeis.org

16, 36, 286, 1348, 7902, 42812, 242438, 1349524, 7567448, 42328892, 237017542, 1326679924, 7427188036, 41577119948, 232754004212, 1302972323234, 7294158727224, 40833303099488, 228588363496794, 1279657095800040

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Row 2 of A218522

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

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

Empirical: a(n) = 2*a(n-1) +17*a(n-2) +26*a(n-3) -19*a(n-4) -123*a(n-5) -138*a(n-6) -248*a(n-7) -329*a(n-8) +41*a(n-9) +1108*a(n-10) +1469*a(n-11) -54*a(n-12) -1158*a(n-13) -316*a(n-14) +144*a(n-15) +32*a(n-16)

A218524 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 3Xn array.

Original entry on oeis.org

64, 236, 4634, 46140, 639228, 7687526, 100029148, 1260284690, 16119079970, 204833380744, 2611281890222, 33242567872546, 423477139656892, 5393125440584082, 68692255949507890, 874885927192766714

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Row 3 of A218522

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

R. H. Hardin, Table of n, a(n) for n = 1..159

A218525 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 4Xn array.

Original entry on oeis.org

256, 1528, 76214, 1608968, 49466988, 1326731972, 38497164700, 1087736452738, 31117471227206, 886142080344254, 25291550132660836, 721303064302959840, 20578939287128886034, 587046975916765583280, 16747555229309088955058

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Row 4 of A218522

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

R. H. Hardin, Table of n, a(n) for n = 1..90

A218526 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 5Xn array.

Original entry on oeis.org

1024, 9858, 1254462, 55161270, 3856183182, 232640291710, 15254005086276, 976050560467866, 63186522328806688, 4074953804995533450, 263247479789131189516, 16998628931896126608784, 1097906084227236452750416

Offset: 1

R. H. Hardin Oct 31 2012

nonn

Row 5 of A218522

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

R. H. Hardin, Table of n, a(n) for n = 1..47

cp's OEIS Frontend

A218516 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 n X 2 array.

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A218517 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 n X 3 array.

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A218518 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX4 array.

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A218519 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX5 array.

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A218520 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX6 array.

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A218521 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 nX7 array.

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A218523 Number of 2Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 2Xn array.

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A218524 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 3Xn array.

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A218525 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 4Xn array.

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A218526 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 5Xn array.

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