A251228 -id:A251228 - cp's OEIS frontend

A251221 Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

14, 49, 171, 597, 2084, 7275, 25396, 88654, 309479, 1080349, 3771351, 13165272, 45958169, 160433700, 560052166, 1955065729, 6824867819, 23824682749, 83168718156, 290330652147, 1013504710004, 3538006716150, 12350698916311

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

Column 1 of A251228.

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

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

Cf. A251228.

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

Empirical g.f.: x*(14 + 7*x - 4*x^2) / (1 - 3*x - 2*x^2 + x^3). - Colin Barker, Feb 25 2018

A251220 Number of (n+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

14, 305, 20782, 4462968, 3007738372, 6373427948731, 42432102644410392, 887822645668106069016, 58374742677350528694024651, 12061621459257582136492647314788, 7831831916823870434473136772446378463

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

Diagonal of A251228.

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

R. H. Hardin, Table of n, a(n) for n = 1..15

Cf. A251228.

A251222 Number of (n+1) X (2+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

49, 305, 1892, 11753, 72985, 453273, 2814985, 17482154, 108570830, 674266427, 4187452312, 26005680486, 161505221644, 1003009195172, 6229070707553, 38684911434209, 240248095245952, 1492032555580773, 9266092805568853

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

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

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

Column 2 of A251228.

Empirical: a(n) = 5*a(n-1) + 9*a(n-2) - 8*a(n-3) - 8*a(n-4) + 3*a(n-5).

Empirical g.f.: x*(49 + 60*x - 74*x^2 - 60*x^3 + 24*x^4) / ((1 - x)*(1 + x)*(1 - 5*x - 8*x^2 + 3*x^3)). - Colin Barker, Nov 27 2018

A251223 Number of (n+1)X(3+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

171, 1892, 20782, 228689, 2515011, 27662994, 304255924, 3346446223, 36806732398, 404828461391, 4452610577279, 48973192395914, 538644351143299, 5924419545393448, 65161264266944558, 716693058210959682

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

Column 3 of A251228

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

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

Empirical: a(n) = 8*a(n-1) +39*a(n-2) -48*a(n-3) -210*a(n-4) +88*a(n-5) +260*a(n-6) -199*a(n-7) +36*a(n-8)

A251224 Number of (n+1)X(4+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

597, 11753, 228689, 4462968, 87024544, 1697323707, 33102432698, 645599385182, 12591115117932, 245564664777825, 4789248769819459, 93404749891139903, 1821673395009104814, 35528107366814113243, 692904893934316841530

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

Column 4 of A251228

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

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

Empirical: a(n) = 13*a(n-1) +150*a(n-2) -269*a(n-3) -3713*a(n-4) +1325*a(n-5) +30575*a(n-6) -16105*a(n-7) -99760*a(n-8) +117265*a(n-9) +20076*a(n-10) -71217*a(n-11) +11160*a(n-12) +14210*a(n-13) -3935*a(n-14) -1079*a(n-15) +396*a(n-16) +60*a(n-17)

A251225 Number of (n+1)X(5+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

2084, 72985, 2515011, 87024544, 3007738372, 103986727042, 3594807908974, 124275144041759, 4296252165879236, 148523812761431640, 5134547519926425245, 177504075991625903000, 6136411350172751480986, 212139042310887309043390

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

Column 5 of A251228

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

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

Empirical: a(n) = 21*a(n-1) +554*a(n-2) -1341*a(n-3) -56723*a(n-4) -7614*a(n-5) +2277951*a(n-6) +445571*a(n-7) -46434220*a(n-8) +32482888*a(n-9) +467723527*a(n-10) -889155765*a(n-11) -1188153000*a(n-12) +4147652079*a(n-13) -132672964*a(n-14) -8042725671*a(n-15) +4499239992*a(n-16) +7457116236*a(n-17) -6933658033*a(n-18) -3126154333*a(n-19) +4558838720*a(n-20) +384337441*a(n-21) -1441277326*a(n-22) +61108155*a(n-23) +221926922*a(n-24) -13300621*a(n-25) -18641195*a(n-26) -491525*a(n-27) +335825*a(n-28) +5625*a(n-29)

A251226 Number of (n+1) X (6+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

7275, 453273, 27662994, 1697323707, 103986727042, 6373427948731, 390586327228567, 23937316421928928, 1466999236798838668, 89905332249468711934, 5509861728752949673273, 337672768681288148069329

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

Column 6 of A251228.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 54

Cf. A251228.

Empirical recurrence of order 54 (see link above).

A251227 Number of (n+1)X(7+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

25396, 2814985, 304255924, 33102432698, 3594807908974, 390586327228567, 42432102644410392, 4609884118941107106, 500818517947942768226, 54409178269320447394874, 5911035284990253460656387

Offset: 1

R. H. Hardin, Nov 30 2014

nonn

Column 7 of A251228

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 99

Empirical recurrence of order 99 (see link above)

cp's OEIS Frontend

A251221 Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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A251220 Number of (n+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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A251222 Number of (n+1) X (2+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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A251223 Number of (n+1)X(3+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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A251224 Number of (n+1)X(4+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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A251225 Number of (n+1)X(5+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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A251226 Number of (n+1) X (6+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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A251227 Number of (n+1)X(7+1) 0..1 arrays with no 2X2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.

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