cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Christopher Hunt Gribble, Jun 12 2012

Keywords

Comments

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.

Examples

			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.

Links

Crossrefs

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

Views

Author

Christopher Hunt Gribble, Jun 12 2012

Keywords

Comments

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.

Examples

			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.

Links

Crossrefs

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

Views

Author

Christopher Hunt Gribble, Jun 12 2012

Keywords

Comments

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.

Examples

			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.

Links

Crossrefs

Cf. A213106, A213249, A213431, A213433, A213473, A213474, A213475.
Showing 1-3 of 3 results.

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