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 1-4 of 4 results.

A213426 Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 9, n >= 2.

Original entry on oeis.org

4, 4, 6, 10, 14, 20, 30, 44, 60, 60, 28, 2, 4, 8, 16, 22, 54, 70, 152, 238, 416, 574, 810, 642, 760, 456, 320, 136, 72, 8, 4, 8, 20, 40, 84, 126, 268, 418, 1014, 1450, 2890, 3510, 5474, 5286, 7238, 6926, 8218, 5636, 6754, 2956, 4220, 778, 48
Offset: 2

Views

Author

Christopher Hunt Gribble, Jun 11 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...25
.n
.2....4....4....6...10...14...20...30...44...60...60...28....2
.3....4....8...16...22...54...70..152..238..416..574..810..642..760..456..320..136...72....8
.4....4....8...20...40...84..126..268..418.1014.1450.2890.3510.5474.5286.7238.6926.8218.5636.6754.2956.4220..778...48
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 <= 10 are 14, 20, 25, 30, 36, 42, 48, 53. Reading this array by rows gives the sequence. One half of the numbers of paths constitute the sequence to remove the effect of the bilateral symmetry of the rectangle.

Examples

			T(2,3) = One half of the number of complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 9 node rectangle.

Links

Crossrefs

Cf. A213106, A213249, A213274, A213089, A213342, A213375, A213379, A213383, A213425.

A214038 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.

Original entry on oeis.org

34, 23, 16, 13, 347, 225, 142, 109, 298, 146, 74, 46, 2347, 1842, 1526, 1387, 2008, 1001, 663, 669, 19287, 16735, 15113, 13878, 6131, 9444, 7697, 8612, 15246, 6758, 5858, 8496, 163666, 141849, 126129, 112049, 132636, 81112, 65551, 67006, 118724, 58677, 60918, 87046
Offset: 2

Views

Author

Christopher Hunt Gribble, Jul 01 2012

Keywords

Comments

The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 4 to capture all geometrically distinct counts.
The quarter-rectangle is read by rows.
The irregular array of numbers is:
...k......1......2......3......4......5......6......7......8......9.....10.....11.....12
.n
.2.......34.....23.....16.....13
.3......347....225....142....109....298....146.....74.....46
.4.....2347...1842...1526...1387...2008...1001....663....669
.5....19287..16735..15113..13878...6131...9444...7697...8612..15246...6758...5858...8496
.6...163666.141849.126129.112049.132636..81112..65551..67006.118724..58677..60918..87046
where k indicates the position of the start node in the quarter-rectangle.
For each n, the maximum value of k is 4*floor((n+1)/2).
Reading this array by rows gives the sequence.

Examples

			When n = 2, the number of times (NT) each node in the rectangle is the start node (SN) of a complete non-self-adjacent simple path is
SN  0  1  2  3  4  5  6  7
    8  9 10 11 12 13 14 15
NT 34 23 16 13 13 16 23 34
   34 23 16 13 13 16 23 34
To limit duplication, only the top left-hand corner 34 and the 23, 16 and 13 to its right are stored in the sequence, i.e. T(2,1) = 34, T(2,2) = 23, T(2,3) = 16 and T(2,4) = 13.

Links

Crossrefs

Cf. A213106, A213249, A213425, A213478, A213954, A214022, A214023, A214025, A214037

A214375 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.

Original entry on oeis.org

86, 0, 0, 0, 747, 119, 124, 109, 12, 0, 0, 0, 5029, 1245, 1624, 1537, 386, 106, 618, 898, 40489, 11359, 15642, 15239, 6345, 1689, 6165, 8214, 7544, 2772, 12824, 16728, 343645, 89102, 125043, 128224, 72452, 12593, 39711, 47539, 80324, 28387, 113790, 134553
Offset: 2

Views

Author

Christopher Hunt Gribble, Jul 14 2012

Keywords

Comments

The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 4 to capture all geometrically distinct counts.
The quarter-rectangle is read by rows.
The irregular array of numbers is:
...k......1......2......3......4......5......6......7......8......9.....10.....11.....12
.n
.2.......86......0......0......0
.3......747....119....124....109.....12......0......0......0
.4.....5029...1245...1624...1537....386....106....618....898
.5....40489..11359..15642..15239...6345...1689...6165...8214...7544...2772..12824..16728
.6...343645..89102.125043.128224..72452..12593..39711..47539..80324..28387.113790.134553
where k indicates the position of the end node in the quarter-rectangle.
For each n, the maximum value of k is 4*floor((n+1)/2).
Reading this array by rows gives the sequence.

Examples

			When n = 2, the number of times (NT) each node in the rectangle is the end node (EN) of a complete non-self-adjacent simple path is
EN  0  1  2  3  4  5  6  7
    8  9 10 11 12 13 14 15
NT 86  0  0  0  0  0  0 86
   86  0  0  0  0  0  0 86
To limit duplication, only the top left-hand corner 86 and the three zeros to its right are stored in the sequence, i.e. T(2,1) = 86, T(2,2) = 0, T(2,3) = 0 and T(2,4) = 0.

Links

Crossrefs

Cf. A213106, A213249, A213425, A214038, A214119, A214121, A214122, A214359, A213070, A214373.

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

A214605 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths incorporating each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.

Original entry on oeis.org

186, 190, 192, 202, 1943, 2219, 2250, 2333, 2170, 2472, 2222, 2200, 18630, 23979, 26077, 26479, 24035, 23261, 20216, 20016, 184991, 259387, 298358, 300853, 269833, 254971, 232802, 232923, 307936, 238766, 178292, 178350
Offset: 2

Views

Author

Christopher Hunt Gribble, Jul 22 2012

Keywords

Comments

The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 4 to capture all geometrically distinct counts.
The quarter-rectangle is read by rows.
The irregular array of numbers is:
...k......1......2......3......4......5......6......7......8......9.....10.....11.....12
.n
.2......186....190....192....202
.3.....1943...2219...2250...2333...2170...2472...2222...2200
.4....18630..23979..26077..26479..24035..23261..20216..20016
.5...184991.259387.298358.300853.269833.254971.232802.232923.307936.238766.178292.178350
where k indicates the position of a node in the quarter-rectangle.
For each n, the maximum value of k is 4*floor((n+1)/2).
Reading this array by rows gives the sequence.

Examples

			When n = 2, the number of times (NT) each node in the rectangle (N) occurs in a complete non-self-adjacent simple path is
N    0   1   2   3   4   5   6   7
     8   9  10  11  12  13  14  15
NT 186 190 192 202 202 192 190 186
   186 190 192 202 202 192 190 186
To limit duplication, only the top left-hand corner 186 and the 190, 192, 202 to its right are stored in the sequence,
i.e. T(2,1) = 186, T(2,2) = 190, T(2,3) = 192 and T(2,4) = 202.

Links

Crossrefs

Cf. A213106, A213249, A213425, A214038, A214375, A214397, A214399, A214504, A214510, A214563, A214601, A214503
Showing 1-4 of 4 results.

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