A213433 -id:A213433 - cp's OEIS frontend

A213473 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2.

2, 4, 6, 6, 2, 4, 10, 18, 8, 8, 14, 2, 4, 10, 18, 20, 12, 18, 8, 42, 2, 4, 10, 22, 46, 66, 60, 56, 106, 72, 236, 26, 2, 4, 10, 22, 50, 100, 152, 158, 230, 246, 410, 260, 546, 124, 32, 2, 4, 10, 22, 50, 104, 194, 300, 444, 542, 840, 650, 1056, 808, 1144, 354, 292, 16

Offset: 2

Christopher Hunt Gribble, Jun 12 2012

The irregular array of numbers is:
...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20
.n
.2....2....4....6....6
.3....2....4...10...18....8....8...14
.4....2....4...10...18...20...12...18....8...42
.5....2....4...10...22...46...66...60...56..106...72..236...26
.6....2....4...10...22...50..100..152..158..230..246..410..260..546..124...32
.7....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354..292...16
where k is the path length in nodes. There is insufficient evidence to attempt to define the irregularity of the array. However, the maximum values of k for 2 <= n <= 12 are 6, 9, 11, 14, 17, 20, 22, 25, 28, 30, 33. Reading this array by rows gives the sequence. The asymptotic sequence for the number of distinct shapes under rotation of the complete non-self-adjacent simple paths of each nodal length k, where n >= k-1, is 2, 4, 10, 22, 50, 104, 198, 354, 710, 1288, 2600 for which there appears to be no obvious formula.

			T(2,3) = The number of distinct shapes under rotation of the complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 4 node rectangle.

Cf. A213106, A213249, A213431, A213433.

A213474 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.

Original entry on oeis.org

2, 4, 6, 10, 10, 2, 2, 4, 10, 22, 34, 22, 36, 22, 18, 2, 4, 10, 22, 46, 66, 60, 56, 106, 72, 236, 26, 2, 4, 10, 22, 46, 66, 100, 76, 132, 116, 314, 160, 654, 124, 28, 2, 4, 10, 22, 50, 100, 192, 318, 340, 430, 726, 816, 1786, 1454, 4626, 1394, 706, 218, 4

Offset: 2

Christopher Hunt Gribble, Jun 12 2012

The irregular array of numbers is:
...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20...21
.n
.2....2....4....6...10...10....2
.3....2....4...10...22...34...22...36...22...18
.4....2....4...10...22...46...66...60...56..106...72..236...26
.5....2....4...10...22...46...66..100...76..132..116..314..160..654..124...28
.6....2....4...10...22...50..100..192..318..340..430..726..816.1786.1454.4626.1394..706..218....4
where k is the path length in nodes. There is insufficient evidence to attempt to define the irregularity of the array. However, the maximum values of k for 2 <= n <= 9 are 8, 11, 14, 17, 21, 24, 27, 30. Reading this array by rows gives the sequence. The asymptotic sequence for the number of distinct shapes under rotation of the complete non-self-adjacent simple paths of each nodal length k for n >= k-1 is 2, 4, 10, 22, 50, 104, 238, 514 for which there appears to be no obvious formula.

			T(2,3) = The number of distinct shapes under rotation of the complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 5 node rectangle.

Cf. A213106, A213249, A213431, A213433, A213473.

A213475 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 6, n >= 2.

Original entry on oeis.org

2, 4, 6, 10, 14, 16, 8, 2, 4, 10, 22, 38, 56, 68, 80, 58, 34, 24, 2, 2, 4, 10, 22, 50, 100, 152, 158, 230, 246, 410, 260, 546, 124, 32, 2, 4, 10, 22, 50, 100, 192, 318, 340, 430, 726, 816, 1786, 1454, 4626, 1394, 706, 218, 4

Offset: 2

Christopher Hunt Gribble, Jun 12 2012

The irregular array of numbers is:
...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20...21
.n
.2....2....4....6...10...14...16....8
.3....2....4...10...22...38...56...68...80...58...34...24....2
.4....2....4...10...22...50..100..152..158..230..246..410..260..546..124...32
.5....2....4...10...22...50..100..192..318..340..430..726..816.1786.1454.4626.1394..706..218....4
where k is the path length in nodes. There is insufficient evidence to attempt to define the irregularity of the array. However, the maximum values of k for 2 <= n <= 7 are 9, 14, 17, 21, 24, 29. Reading this array by rows gives the sequence. The asymptotic sequence for the number of distinct shapes under rotation of the complete non-self-adjacent simple paths of each nodal length k for n >= k-1 is 2, 4, 10, 22, 50, 104 for which there appears to be no obvious formula.

			T(2,3) = The number of distinct shapes under rotation of the complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 6 node rectangle.

Cf. A213106, A213249, A213431, A213433, A213473, A213474.

A213476 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 7, n >= 2.

Original entry on oeis.org

2, 4, 6, 10, 14, 20, 26, 18, 2, 2, 4, 10, 22, 38, 60, 110, 138, 188, 106, 108, 54, 36, 4, 2, 4, 10, 22, 50, 104, 194, 300, 444, 542, 840, 650, 1056, 808, 1144, 354, 292, 16, 2, 4, 10, 22, 50, 104, 234, 460, 778, 894, 1540, 1812, 3444, 3512, 8294, 6104, 13914, 5778, 5548, 2216, 710, 24

Offset: 2

Christopher Hunt Gribble, Jun 12 2012

The irregular array of numbers is:
...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18....19...20...21...22...23...24
.n
.2....2....4....6...10...14...20...26...18....2
.3....2....4...10...22...38...60..110..138..188..106..108...54...36....4
.4....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354...292...16
.5....2....4...10...22...50..104..234..460..778..894.1540.1812.3444.3512.8294.6104.13914.5778.5548.2216..710...24
where k is the path length in nodes. There is insufficient evidence to attempt to define the irregularity of the array. However, the maximum values of k for 2 <= n <= 7 are 11, 16, 20, 24, 29, 33. Reading this array by rows gives the sequence. The asymptotic sequence for the number of distinct shapes under rotation of the complete non-self-adjacent simple paths of each nodal length k for n >= k-1 is 2, 4, 10, 22, 50, 104 for which there appears to be no obvious formula.

			T(2,3) = The number of distinct shapes under rotation of the complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 7 node rectangle.

Cf. A213106, A213249, A213431, A213433, A213473, A213474, A213475.

cp's OEIS Frontend

A213473 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2.

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A213474 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.

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A213475 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 6, n >= 2.

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A213476 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 7, n >= 2.

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Author

Keywords

Comments

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