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 1-6 of 6 results.

A214025 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 6, n >= 2.

Original entry on oeis.org

13, 10, 8, 77, 51, 38, 68, 36, 20, 330, 266, 248, 300, 145, 96, 1580, 1381, 1365, 1414, 813, 652, 1402, 596, 432, 7678, 6630, 6357, 6630, 3968, 3192, 6357, 3192, 2828, 35971, 30070, 27638, 30709, 18037, 13744, 27591, 14507, 13851, 26574, 15318, 17846
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 3 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.......13....10.....8
..3.......77....51....38....68....36....20
..4......330...266...248...300...145....96
..5.....1580..1381..1365..1414...813...652..1402...596...432
..6.....7678..6630..6357..6630..3968..3192..6357..3192..2828
..7....35971.30070.27638.30709.18037.13744.27591.14507.13851.26574.15318.17846
where k indicates the position of the start node in the quarter-rectangle.
For each n, the maximum value of k is 3*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
NT 13 10  8  8 10 13
   13 10  8  8 10 13
To limit duplication, only the top left-hand corner 13 and the 10 and 8 to its right are stored in the sequence, i.e. T(2,1) = 13, T(2,2) = 10 and T(2,3) = 8.

Links

Crossrefs

Cf. A213106, A213249, A213375, A213478, A213954, A214022, A214023

A214359 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 5, n >= 2.

Original entry on oeis.org

18, 0, 0, 75, 13, 16, 6, 0, 0, 256, 67, 88, 52, 14, 32, 932, 246, 308, 246, 80, 130, 308, 130, 288, 3431, 746, 920, 992, 251, 352, 1179, 580, 1210, 12027, 2143, 2612, 3522, 640, 954, 4399, 1941, 3956, 4170, 2394, 5136, 40489, 6345, 7544, 11359, 1689, 2772, 15642, 6165, 12824, 15239, 8214, 16728
Offset: 2

Views

Author

Christopher Hunt Gribble, Jul 13 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 3 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......18.....0.....0
.3......75....13....16.....6.....0.....0
.4.....256....67....88....52....14....32
.5.....932...246...308...246....80...130...308...130...288
.6....3431...746...920...992...251...352..1179...580..1210
.7...12027..2143..2612..3522...640...954..4399..1941..3956..4170..2394..5136
.8...40489..6345..7544.11359..1689..2772.15642..6165.12824.15239..8214.16728
where k indicates the position of the end node in the quarter-rectangle.
For each n, the maximum value of k is 3*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
NT 18  0  0  0 18
   18  0  0  0 18
To limit duplication, only the top left-hand corner 18 and the two zeros to its right are stored in the sequence, i.e. T(2,1) = 10, T(2,2) = 0 and T(2,3) = 0.

Links

Crossrefs

Cf. A213106, A213249, A213375, A214023, A214119, A214121, A214122.

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

A214037 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 7, n >= 2.

Original entry on oeis.org

21, 15, 11, 10, 164, 106, 72, 64, 142, 72, 38, 28, 888, 695, 607, 602, 780, 385, 258, 270, 5600, 4795, 4453, 4412, 4829, 2792, 2285, 2556, 4650, 2036, 1712, 2248, 35971, 30709, 27591, 26574, 30070, 18037, 14507, 15318, 27638, 13744, 13851, 17846
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.......21....15....11....10
.3......164...106....72....64....142...72....38....28
.4......888...695...607...602...780...385...258...270
.5.....5600..4795..4453..4412..4829..2792..2285..2556..4650..2036..1712..2248
.6....35971.30709.27591.26574.30070.18037.14507.15318.27638.13744.13851.17846
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
NT 21 15 11 10 11 15 21
   21 15 11 10 11 15 21
To limit duplication, only the top left-hand corner 21 and the 15, 11 and 10 to its right are stored in the sequence, i.e. T(2,1) = 21, T(2,2) = 15, T(2,3) = 11 and T(2,4) = 10.

Links

Crossrefs

Cf. A213106, A213249, A213379, A213478, A213954, A214022, A214023, A214025

A214563 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 5, n >= 2.

Original entry on oeis.org

40, 42, 40, 188, 209, 204, 210, 228, 204, 820, 1007, 1058, 1008, 907, 776, 3426, 4601, 5076, 4601, 4104, 3608, 5076, 3608, 2608, 13344, 18726, 21050, 18302, 17364, 15896, 21307, 15275, 11148, 50036, 71736, 81276, 69029, 67670, 63148, 80263, 61229, 46550, 82942, 60116, 44196
Offset: 2

Views

Author

Christopher Hunt Gribble, Jul 21 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 3 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......40....42....40
.3.....188...209...204...210...228...204
.4.....820..1007..1058..1008...907...776
.5....3426..4601..5076..4601..4104..3608..5076..3608..2608
.6...13344.18726.21050.18302.17364.15896.21307.15275.11148
.7...50036.71736.81276.69029.67670.63148.80263.61229.46550.82942.60116.44196
where k indicates the position of a node in the quarter-rectangle.
For each n, the maximum value of k is 3*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
NT 40 42 40 42 40
   40 42 40 42 40
To limit duplication, only the top left-hand corner 40 and the 42 and 40 to its right are stored in the sequence,
i.e. T(2,1) = 40, T(2,2) = 42 and T(2,3) = 40.

Links

Crossrefs

Cf. A213106, A213249, A213375, A214023, A214359, A214397, A214399, A214504, A214510

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

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

A214042 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 9, n >= 2.

Original entry on oeis.org

55, 36, 24, 18, 16, 732, 476, 294, 197, 168, 628, 302, 148, 82, 64, 6115, 4840, 3979, 3349, 3076, 5170, 2597, 1718, 1595, 1564, 64904, 57210, 52820, 46787, 43294, 53478, 31544, 26459, 28472, 28700, 50228, 22432, 19802, 27924, 30696
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 5 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....13....14....15
.n
.2......55....36....24....18....16
.3.....732...476...294...197...168...628...302...148....82....64
.4....6115..4840..3979..3349..3076..5170..2597..1718..1595..1564
.5...64904.57210.52820.46787.43294.53478.31544.26459.28472.28700.50228.22432.19802.27924.30696
where k indicates the position of the start node in the quarter-rectangle.
For each n, the maximum value of k is 5*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 16 17
NT 55 36 24 18 16 18 24 36 55
   55 36 24 18 16 18 24 36 55
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, A213426, A213478, A213954, A214022, A214023, A214025, A214037, A214038

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012
Showing 1-6 of 6 results.

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