A194615 -id:A194615 - cp's OEIS frontend

A194609 Half the number of lower triangles of an (n+1) X (n+1) 0..2 array with no element equal to the average of its horizontal and vertical neighbors.

5, 96, 4322, 571364, 205801866, 202803700252, 547917448108462, 4059864930297777162, 82468548660331834255159, 4592574521519240269995632810, 701184800636550713667143286769980

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

			Some solutions for 3X3
..1......1......0......0......0......2......1......2......0......2......0
..0.2....2.2....1.2....1.0....2.0....0.1....0.2....1.0....1.0....0.2....2.2
..2.0.2..0.0.2..2.1.2..2.1.2..2.1.0..1.0.1..0.1.0..2.0.2..0.0.1..1.0.1..2.0.1

R. H. Hardin, Table of n, a(n) for n = 1..12

Column 2 of A194615.

A194616 Half the number of lower triangles of a 3X3 0..n array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

5, 96, 775, 3638, 12438, 34247, 82057, 175111, 344173, 630849, 1094898, 1812250, 2887675, 4445870, 6653357, 9703428, 13843860, 19356297, 26596343, 35955433, 47921851, 63027619, 81920692, 105300352, 134012453, 168951880, 211194991

Offset: 1

R. H. Hardin Aug 30 2011

nonn

Row 2 of A194615

			Some solutions for n=2
..2......2......1......1......1......2......0......1......2......0......2
..0.2....1.0....0.2....0.2....2.2....0.2....2.0....0.2....0.2....1.0....1.1
..1.0.1..0.1.2..2.1.0..1.0.1..0.1.0..2.0.2..0.2.0..1.1.2..1.1.2..2.1.2..1.0.1

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = -a(n-1) +a(n-3) +2*a(n-4) +3*a(n-5) +3*a(n-6) +a(n-7) -2*a(n-8) -5*a(n-9) -6*a(n-10) -6*a(n-11) -2*a(n-12) +2*a(n-13) +5*a(n-14) +7*a(n-15) +6*a(n-16) +2*a(n-17) -2*a(n-18) -4*a(n-19) -4*a(n-20) -a(n-21) +a(n-22) +4*a(n-23) +4*a(n-24) +2*a(n-25) -2*a(n-26) -6*a(n-27) -7*a(n-28) -5*a(n-29) -2*a(n-30) +2*a(n-31) +6*a(n-32) +6*a(n-33) +5*a(n-34) +2*a(n-35) -a(n-36) -3*a(n-37) -3*a(n-38) -2*a(n-39) -a(n-40) +a(n-42) +a(n-43)

A194617 Half the number of lower triangles of a 4 X 4 0..n array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

47, 4322, 132214, 1674043, 12561823, 66369488, 279618492, 975189851, 2972844263, 8086809479, 20111108169, 46277171169, 100029289052, 204344500677, 398372414831, 744412292078, 1341415693780, 2338177034539, 3960008651919

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

			Some solutions for n=2
..1........1........0........1........1........1........2........0
..0.1......0.2......2.2......2.0......2.2......2.2......0.2......2.0
..0.1.0....1.2.0....0.0.2....1.2.1....1.1.0....0.0.1....1.1.0....0.1.1
..0.2.2.0..2.0.0.1..1.0.0.2..0.0.2.1..1.2.0.2..1.0.0.1..1.0.0.1..2.0.2.1

R. H. Hardin, Table of n, a(n) for n = 1..50

Row 3 of A194615.

A194618 Half the number of lower triangles of a 5 X 5 0..n array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

849, 571364, 86867366, 3703163910, 73569838704, 873084601728, 7416076339907, 47683223919057, 251059904306865, 1116910109397146, 4348691274427714, 15090969268080476, 47709109611064061, 138700124724207796

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

			Some solutions for n=2
..0..........0..........0..........0..........0..........0..........0
..2.0........2.0........2.0........1.0........2.0........1.0........2.0
..2.0.2......0.2.0......0.1.0......1.0.1......0.2.1......1.0.2......0.1.0
..2.2.0.1....1.2.2.0....1.1.0.1....0.1.1.2....0.1.2.0....1.0.0.0....2.2.2.0
..1.1.1.1.2..2.2.1.0.1..0.0.2.1.2..0.1.1.0.1..2.2.0.2.0..0.1.0.2.0..0.2.0.0.2

R. H. Hardin, Table of n, a(n) for n = 1..18

Row 4 of A194615.

A194610 Half the number of lower triangles of an (n+1) X (n+1) 0..3 array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

16, 775, 132214, 86867366, 214726600125, 1988649454264015, 69098146174647014753, 9010212831798851496619501, 4408846076603948466494884939778

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

Column 3 of A194615.

			Some solutions for 3 X 3
..1......3......1......3......0......0......2......3......3......3......1
..2.1....0.1....2.1....1.0....2.3....2.0....0.0....2.1....0.3....2.0....0.3
..2.1.2..1.3.2..3.1.3..2.1.0..0.0.2..2.0.3..2.1.3..1.1.2..3.0.2..2.3.0..2.3.1

Cf. A194615.

A194611 Half the number of lower triangles of an (n+1) X (n+1) 0..4 array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

36, 3638, 1674043, 3703163910, 38969955227338, 1946585305112431165, 461761593540314858209528, 520265339158575595235640177020

Offset: 1

R. H. Hardin, Aug 30 2011

			Some solutions for 3X3
..3......2......2......0......1......4......4......3......1......3......1
..0.4....0.3....4.2....3.1....2.2....0.1....1.1....4.0....2.3....1.0....4.4
..1.3.1..4.0.3..4.2.1..4.1.4..2.3.1..0.3.0..4.2.3..3.1.4..0.1.2..1.3.2..2.3.0

Column 4 of A194615.

A194612 Half the number of lower triangles of an (n+1) X (n+1) 0..5 array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

69, 12438, 12561823, 73569838704, 2481372954501732, 481414314393133400117

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

			Some solutions for 3X3
..0......0......3......3......1......2......2......5......4......2......1
..2.0....4.3....0.0....0.3....4.4....5.0....1.0....1.1....0.2....1.2....0.5
..1.5.2..0.4.0..0.4.3..4.1.2..5.0.5..2.4.0..0.4.5..2.5.1..4.2.4..4.1.2..2.5.4

Column 5 of A194615.

A194613 Half the number of lower triangles of an (n+1) X (n+1) 0..6 array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

117, 34247, 66369488, 873084601728, 77572756670578163, 46519509694797259637061

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

			Some solutions for 3X3
..3......6......3......1......3......5......1......4......1......4......6
..1.2....1.2....4.4....6.0....2.3....2.5....0.5....3.1....5.0....5.4....5.4
..2.0.6..1.4.5..3.5.2..0.5.1..1.3.0..2.4.1..6.0.2..2.4.5..5.6.4..6.6.4..0.1.2

Column 6 of A194615.

A194614 Half the number of lower triangles of an (n+1) X (n+1) 0..7 array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

184, 82057, 279618492, 7416076339907, 1525002446582690839, 2430369828996738172677912

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

Column 7 of A194615.

			Some solutions for 3 X 3
..6......0......5......0......2......1......4......7......6......4......0
..4.1....1.4....6.5....2.6....0.1....2.6....0.6....4.2....5.4....3.6....6.4
..1.6.5..7.5.2..4.0.5..1.5.7..0.6.2..4.3.1..0.6.4..0.6.3..3.7.6..1.2.7..1.7.6

Cf. A194615.

A194619 Half the number of lower triangles of a 6 X 6 0..n array with no element equal to the average of its horizontal and vertical neighbors.

Original entry on oeis.org

29241, 205801866, 214726600125, 38969955227338, 2481372954501732, 77572756670578163, 1525002446582690839, 20406859321612678912, 206774026729010778294, 1658596651668908616516, 11050418508749912011440

Offset: 1

R. H. Hardin, Aug 30 2011

nonn

			Some solutions for n=2
..0............0............0............0............0............0
..1.0..........1.0..........1.0..........1.0..........1.0..........1.0
..0.0.2........0.0.1........0.0.1........0.0.1........0.0.1........0.0.1
..0.0.0.0......0.0.0.2......0.0.1.0......0.0.0.0......0.0.1.2......0.0.0.2
..1.1.0.1.0....1.1.2.0.0....1.0.0.1.0....2.2.0.1.0....2.1.0.2.2....1.2.0.2.1
..1.0.1.0.0.2..1.0.0.2.2.1..2.1.2.2.0.1..0.0.0.1.1.0..0.1.0.1.0.2..2.2.0.2.1.2

Row 5 of A194615.

cp's OEIS Frontend

A194609 Half the number of lower triangles of an (n+1) X (n+1) 0..2 array with no element equal to the average of its horizontal and vertical neighbors.

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A194616 Half the number of lower triangles of a 3X3 0..n array with no element equal to the average of its horizontal and vertical neighbors.

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A194617 Half the number of lower triangles of a 4 X 4 0..n array with no element equal to the average of its horizontal and vertical neighbors.

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A194618 Half the number of lower triangles of a 5 X 5 0..n array with no element equal to the average of its horizontal and vertical neighbors.

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A194610 Half the number of lower triangles of an (n+1) X (n+1) 0..3 array with no element equal to the average of its horizontal and vertical neighbors.

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A194611 Half the number of lower triangles of an (n+1) X (n+1) 0..4 array with no element equal to the average of its horizontal and vertical neighbors.

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A194612 Half the number of lower triangles of an (n+1) X (n+1) 0..5 array with no element equal to the average of its horizontal and vertical neighbors.

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A194613 Half the number of lower triangles of an (n+1) X (n+1) 0..6 array with no element equal to the average of its horizontal and vertical neighbors.

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A194614 Half the number of lower triangles of an (n+1) X (n+1) 0..7 array with no element equal to the average of its horizontal and vertical neighbors.

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Comments

Examples

Crossrefs

A194619 Half the number of lower triangles of a 6 X 6 0..n array with no element equal to the average of its horizontal and vertical neighbors.

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