A190071 -id:A190071 - cp's OEIS frontend

A190063 Number of arrangements of n+1 nonzero numbers x(i) in -n..n with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

0, 12, 166, 3481, 88509, 2783714, 101530262, 4232955454, 198636188057, 10408538943146, 603033909983829, 38103929980500423, 2608648993698684772, 193359775333060165517, 15364574547397697984616, 1301880431718317296701496

Offset: 1

R. H. Hardin May 04 2011

nonn

Diagonal of A190071

			Some solutions for n=4
..4...-1...-2....1...-1...-4....4...-3...-2...-4...-3...-3....4...-1....2...-2
..4...-2...-1....1....2...-4....1...-2...-3....2....1....4....2....1....2...-1
.-2....1...-2....3...-4...-2...-3...-1...-4....2...-4...-2...-2...-1....2...-3
.-1....3....2...-4....4....1....2....3....2...-2...-2...-1....2...-2....4....2
..1....2...-1....4....2...-1...-1...-1....3...-1...-2...-2...-4...-2...-2...-2

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

A190064 Number of arrangements of n+1 nonzero numbers x(i) in -2..2 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

2, 12, 40, 144, 550, 1896, 7584, 27328, 105348, 398760, 1538696, 5872800, 22646862, 87492676, 339055650, 1313842904, 5104724558, 19873572892, 77470783406, 302258087616, 1180840902336, 4618922848536, 18083348822516, 70852652846320

Offset: 1

R. H. Hardin May 04 2011

nonn

Column 2 of A190071

			Some solutions for n=4
.-2...-1...-1...-2...-2....1....2...-1...-1....2...-2....1....2....2....1....1
.-2....1....1...-1...-1...-1....1....1...-2...-1....1....1...-1....2...-2....1
..2....1...-2....1....1...-1....2....2....1...-2....1....2....2....2....1....1
.-2...-1....2....2...-2....2...-2...-2....1....2....1...-1....1...-2....2...-1
.-2...-2....1...-2....2....2....2...-1....2....1....2...-1....1....2....1....1

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

A190065 Number of arrangements of n+1 nonzero numbers x(i) in -3..3 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

6, 36, 166, 922, 5136, 28656, 162028, 910716, 5162308, 29554964, 169886511, 978214225, 5650347932, 32745824773, 190185910978, 1106505067832, 6449387884888, 37654438607875, 220148079884339, 1288689800220653

Offset: 1

R. H. Hardin May 04 2011

nonn

Column 3 of A190071

			Some solutions for n=4
.-1...-2....2...-2...-1...-1....3....2....1....2...-1....2...-3....2....2...-1
..3...-3....1....3...-3...-1...-2....1....1....2....1...-3....3....1...-2...-1
..3....2...-1...-2...-3....1...-1...-1....1....3...-3...-3...-1...-1...-2...-1
.-2....1....1...-2....2....2....2....2...-1....2...-2...-3...-3...-3...-2....1
.-2...-1...-2...-2....3....3....3...-3....1...-1....2....2...-1....2....2...-1

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

A190066 Number of arrangements of n+1 nonzero numbers x(i) in -4..4 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

12, 76, 483, 3481, 25306, 191456, 1436962, 10802667, 81709584, 622881909, 4769974211, 36631166224, 282173132213, 2179898773167, 16878487835945, 130935467642770, 1017555976447868, 7920656405513158, 61741451812499715

Offset: 1

R. H. Hardin May 04 2011

nonn

Column 4 of A190071

			Some solutions for n=5
..3...-2....2....3...-1....3...-1...-2...-4...-1...-1....3...-1....1...-3....4
.-1....2....2....3...-2...-3....2...-4...-4....2...-4....3....2....4....4...-2
.-2....3...-4...-3...-4...-1....3...-1....3....4....1....3...-4...-3...-3....3
.-2....3....4...-2...-4....2....1....2....1....2....2...-3....3....3...-4....2
.-1...-2....3....3....2...-4...-1...-4...-4....2....2....3....1...-4...-2....1
..3...-4...-2...-2...-2....4....1....1....3...-1....1....4....2...-2....2...-4

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

A190067 Number of arrangements of n+1 nonzero numbers x(i) in -5..5 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

20, 143, 1126, 9904, 88509, 834717, 7843113, 73725405, 697624797, 6644826507, 63556636483, 609902716100, 5871497904831, 56683948490522, 548487091412193, 5317814454716839, 51651465543152430, 502495332741155890

Offset: 1

R. H. Hardin May 04 2011

nonn

Column 5 of A190071

			Some solutions for n=4
.-3....5....1...-1....1....2....3....4...-4....4....2...-5....4....1...-5....4
..4...-3...-3...-2....2...-4...-2....1...-3...-3....1...-5...-5...-5....5...-1
..1....5....3...-3...-3....2...-2....3....3....4...-5....3...-2...-3...-5...-3
..3....4...-5....2....2....1...-3...-1....5...-5....3...-3....1....2...-2...-5
.-1....4...-5...-3....1...-2....5....1...-3...-3....5...-2...-1....5....5...-3

R. H. Hardin, Table of n, a(n) for n = 1..137

A190068 Number of arrangements of n+1 nonzero numbers x(i) in -6..6 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

30, 233, 2276, 23400, 249119, 2783714, 31391655, 353856100, 4017545773, 45918810745, 526830982562, 6064138473938, 70033913982429, 811112118405079, 9415846493673903, 109526722276860886, 1276368965090149581

Offset: 1

R. H. Hardin May 04 2011

nonn

Column 6 of A190071

			Some solutions for n=4
..4...-6....1...-3...-5...-1...-4...-2...-4...-5....2....4...-5....1....4....1
.-5....4...-5...-6....2....4...-4...-5....3...-5...-5...-3....3...-3...-5....3
.-4...-5...-5....5...-4...-2...-6....3....6....6....4...-5....6....3...-4....5
..6...-2....5....4...-5...-4....4....3....6....6....2....5....4....2....3....5
.-4....2...-6....5...-3...-2...-5...-4....6...-6...-6....4....3...-3...-5...-3

R. H. Hardin, Table of n, a(n) for n = 1..125

A190069 Number of arrangements of n+1 nonzero numbers x(i) in -7..7 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

42, 366, 4150, 48491, 599181, 7737762, 101530262, 1333341624, 17643516841, 235162515839, 3146321736755, 42232649776342, 568807797004946, 7683091138249061, 104022021281511319, 1411291383524511348

Offset: 1

R. H. Hardin May 04 2011

nonn

Column 7 of A190071

			Some solutions for n=4
..5....3...-4...-5....7....3....1....1....5...-3....3....1...-4....2....4....5
.-5....5...-6...-5....3...-2...-3....2...-1...-2...-3...-5...-2...-3....6...-1
.-5...-3...-7...-7...-2...-7...-3....6....3....1....6....3...-7....2...-5...-1
..7...-2....4....7....2...-5...-4....6....6....2....4...-7....6....1...-3...-7
..5....4....5...-6...-3....4....3...-5....1....7....4...-5...-5...-4....5...-3

R. H. Hardin, Table of n, a(n) for n = 1..81

A190070 Number of arrangements of n+1 nonzero numbers x(i) in -8..8 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

56, 536, 6946, 92478, 1291797, 18951546, 282859251, 4232955454, 63898862902, 972408511316, 14859125421285, 227805216299376, 3504714306481893, 54079878634478640, 836480995724826396, 12965711458798193610

Offset: 1

R. H. Hardin May 04 2011

nonn

Column 8 of A190071

			Some solutions for n=4
..7....8....8....5...-3...-6...-2...-2...-7....2....3...-7...-8....5....8...-3
..6....3....2....8...-8....4...-3....6....8...-5...-7...-6....8....2....8....5
.-2....5...-4....8....6....3....6...-8....8...-3....3....8....8...-6...-4...-3
.-3...-8....1...-4....5....3....6....7....5....5....1....5....7....4....6...-4
.-6....7...-8...-7....8....6...-4....2...-4...-3...-7...-2...-7...-6....3...-6

R. H. Hardin, Table of n, a(n) for n = 1..76

A190072 Number of arrangements of 3 nonzero numbers x(i) in -n..n with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

4, 12, 36, 76, 143, 233, 366, 536, 760, 1028, 1363, 1751, 2221, 2758, 3387, 4096, 4907, 5804, 6819, 7931, 9174, 10525, 12021, 13631, 15401, 17299, 19366, 21572, 23959, 26490, 29220, 32114, 35210, 38476, 41963, 45629, 49527, 53618, 57953, 62489, 67285

Offset: 1

R. H. Hardin, May 04 2011

nonn

Row 2 of A190071.

			Some solutions for n=4
.-1....1....4...-2...-1....1...-3...-4...-2...-1...-1....2...-4...-3....3....1
..3...-1...-4...-4....1....3...-3...-3....3...-3...-1....2...-2....4...-3...-1
..2...-3...-4....4....1....4....3....2....2....4....1...-2....1....4...-4...-2

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

Cf. A190071.

A190073 Number of arrangements of 4 nonzero numbers x(i) in -n..n with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

Original entry on oeis.org

0, 40, 166, 483, 1126, 2276, 4150, 6946, 10909, 16353, 23728, 33290, 45591, 61100, 80161, 103121, 130833, 163649, 202441, 247746, 300269, 360694, 430361, 508989, 598090, 698534, 811133, 936287, 1075989, 1230312, 1401309, 1589246, 1795222

Offset: 1

R. H. Hardin May 04 2011

nonn

Row 3 of A190071

			Some solutions for n=4
..4...-3...-3...-4....2...-4...-1...-1...-1...-4...-4....3....2....3...-2....1
.-4....3....3....1....3....3...-1....4....3...-3...-4....3...-1...-1...-4....4
..3....3....3....4...-2...-4...-3...-4....2....2...-4....2...-1...-4...-4...-3
..1...-4....4....1...-3...-3....2...-2....3....3....3...-1...-1...-3....3...-3

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

cp's OEIS Frontend

A190063 Number of arrangements of n+1 nonzero numbers x(i) in -n..n with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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A190064 Number of arrangements of n+1 nonzero numbers x(i) in -2..2 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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A190065 Number of arrangements of n+1 nonzero numbers x(i) in -3..3 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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A190066 Number of arrangements of n+1 nonzero numbers x(i) in -4..4 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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A190067 Number of arrangements of n+1 nonzero numbers x(i) in -5..5 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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A190068 Number of arrangements of n+1 nonzero numbers x(i) in -6..6 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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A190069 Number of arrangements of n+1 nonzero numbers x(i) in -7..7 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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A190070 Number of arrangements of n+1 nonzero numbers x(i) in -8..8 with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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Author

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Comments

Examples

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A190072 Number of arrangements of 3 nonzero numbers x(i) in -n..n with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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Author

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A190073 Number of arrangements of 4 nonzero numbers x(i) in -n..n with the sum of div(x(i),x(i+1)), where div(a,b)=a/b produces the integer quotient implying a nonnegative remainder, equal to zero.

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