A218064 -id:A218064 - cp's OEIS frontend

A218059 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 n X 3 array.

4, 18, 74, 308, 1282, 5338, 22228, 92562, 385450, 1605108, 6684066, 27834106, 115908116, 482670130, 2009958090, 8369963828, 34854604610, 145143215386, 604412335444, 2516922821842, 10481090672106, 43645860224116

Offset: 1

R. H. Hardin, Oct 19 2012

nonn

Column 3 of A218064.

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

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

Cf. A218064.

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

Empirical g.f.: 2*x*(2 - x - 2*x^2) / (1 - 5*x + 3*x^2 + 2*x^3). - Colin Barker, Mar 09 2018

A218060 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 n X 4 array.

Original entry on oeis.org

6, 42, 260, 1664, 10566, 66978, 424332, 2687866, 17025060, 107835994, 683025864, 4326234664, 27402037744, 173562384900, 1099330676692, 6963075143418, 44103577188722, 279348632561274, 1769372542444278, 11207068261293544

Offset: 1

R. H. Hardin, Oct 19 2012

nonn

Column 4 of A218064.

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

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

Cf. A218064.

Empirical: a(n) = 9*a(n-1) - 18*a(n-2) + 6*a(n-3) + 7*a(n-4) - 2*a(n-5) - a(n-6) for n>7.

Empirical g.f.: 2*x*(3 - 6*x - 5*x^2 + 22*x^3 - 12*x^4 - 3*x^5 + 2*x^6) / ((1 - x)*(1 - 8*x + 10*x^2 + 4*x^3 - 3*x^4 - x^5)). - Colin Barker, Jul 23 2018

A218061 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nX5 array.

Original entry on oeis.org

10, 108, 1046, 10246, 99934, 975296, 9519284, 92918894, 907013406, 8853740672, 86425318934, 843636853718, 8235125319032, 80386833101166, 784692748485262, 7659745900162448, 74770293910981462, 729867143111233166

Offset: 1

R. H. Hardin Oct 19 2012

nonn

Column 5 of A218064

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

R. H. Hardin, Table of n, a(n) for n = 1..158

Empirical: a(n) = 15*a(n-1) -56*a(n-2) +37*a(n-3) +117*a(n-4) -132*a(n-5) -128*a(n-6) +164*a(n-7) +60*a(n-8) -76*a(n-9) -4*a(n-10) +8*a(n-11) for n>13

A218062 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nX6 array.

Original entry on oeis.org

16, 268, 3974, 60804, 925904, 14096488, 214514380, 3263893360, 49658510202, 755518606946, 11494629017172, 174881679122376, 2660685599023984, 40480211800235302, 615874165289837908, 9370034622516193552

Offset: 1

R. H. Hardin Oct 19 2012

nonn

Column 6 of A218064

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

R. H. Hardin, Table of n, a(n) for n = 1..72

Empirical: a(n) = 26*a(n-1) -199*a(n-2) +527*a(n-3) +257*a(n-4) -3086*a(n-5) +918*a(n-6) +11050*a(n-7) -6781*a(n-8) -25737*a(n-9) +23534*a(n-10) +29646*a(n-11) -36015*a(n-12) -15207*a(n-13) +25338*a(n-14) +2853*a(n-15) -8912*a(n-16) +2728*a(n-17) -200*a(n-18) +36*a(n-19) -16*a(n-20) for n>21

A218063 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nX7 array.

Original entry on oeis.org

26, 676, 15578, 368220, 8679594, 204211050, 4803404048, 112984025006, 2657601417086, 62512388662498, 1470427119098160, 34587669928567490, 813578051651191626, 19137146231249558584, 450147804547520272046

Offset: 1

R. H. Hardin Oct 19 2012

nonn

Column 7 of A218064

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

R. H. Hardin, Table of n, a(n) for n = 1..34

A218065 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 2 X n array.

Original entry on oeis.org

4, 6, 18, 42, 108, 268, 676, 1694, 4258, 10690, 26852, 67436, 169372, 425382, 1068370, 2683258, 6739132, 16925644, 42509556, 106764750, 268144706, 673458066, 1691421684, 4248085292, 10669266476, 26796365718, 67300335730, 169027965834

Offset: 1

R. H. Hardin, Oct 19 2012

nonn

Row 2 of A218064.

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

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

Cf. A218064.

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

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

A218066 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 3Xn array.

Original entry on oeis.org

8, 16, 74, 260, 1046, 3974, 15578, 60242, 234468, 910060, 3536762, 13737348, 53371468, 207332364, 805465810, 3129084596, 12156035112, 47224200410, 183458638422, 712707497212, 2768755861210, 10756176540402, 41786039888224

Offset: 1

R. H. Hardin Oct 19 2012

nonn

Row 3 of A218064

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

R. H. Hardin, Table of n, a(n) for n = 1..170

Empirical: a(n) = 2*a(n-1) +11*a(n-2) -7*a(n-3) -34*a(n-4) +11*a(n-5) +49*a(n-6) -14*a(n-7) -36*a(n-8) +7*a(n-9) +a(n-10) +8*a(n-11) +2*a(n-12) -13*a(n-13) +2*a(n-14) +4*a(n-15) for n>18

A218067 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 4Xn array.

Original entry on oeis.org

16, 42, 308, 1664, 10246, 60804, 368220, 2217012, 13380802, 80716652, 487004728, 2938281242, 17727888682, 106960361186, 645338542928, 3893618011484, 23491925716860, 141737303076720, 855164357481732, 5159588643396442

Offset: 1

R. H. Hardin Oct 19 2012

nonn

Row 4 of A218064

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

R. H. Hardin, Table of n, a(n) for n = 1..70

A218068 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 5Xn array.

Original entry on oeis.org

32, 110, 1282, 10566, 99934, 925904, 8679594, 81335528, 762520474, 7151998338, 67068725044, 629057470766, 5899646647922, 55332856437260, 518956048374100, 4867244207768978, 45649230875835138, 428139074698478122

Offset: 1

R. H. Hardin Oct 19 2012

nonn

Row 5 of A218064

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

R. H. Hardin, Table of n, a(n) for n = 1..56

A218069 Number of 6Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 6Xn array.

Original entry on oeis.org

64, 288, 5338, 66978, 975296, 14096488, 204211050, 2978543964, 43337429212, 631708431924, 9201998558182, 134096314110712, 1953815660270370, 28469970831713488, 414834864922566790, 6044649160655242312

Offset: 1

R. H. Hardin Oct 19 2012

nonn

Row 6 of A218064

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

R. H. Hardin, Table of n, a(n) for n = 1..49

cp's OEIS Frontend

A218059 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 n X 3 array.

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A218060 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 n X 4 array.

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A218061 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nX5 array.

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A218062 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nX6 array.

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A218063 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nX7 array.

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A218065 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 2 X n array.

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A218066 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 3Xn array.

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A218067 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 4Xn array.

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A218068 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 5Xn array.

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A218069 Number of 6Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 6Xn array.

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