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.

A214373 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 7, n >= 2.

Original entry on oeis.org

52, 0, 0, 0, 353, 57, 62, 60, 10, 0, 0, 0, 1931, 495, 622, 602, 200, 56, 262, 364, 12027, 3522, 4399, 4170, 2143, 640, 1941, 2394, 2612, 954, 3956, 5136, 76933, 21068, 26181, 25090, 17601, 3675, 9258, 10048, 20009, 7213, 26414, 32132
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......52.....0.....0.....0
.3.....353....57....62....60....10.....0.....0.....0
.4....1931...495...622...602...200....56...262...364
.5...12027..3522..4399..4170..2143...640..1941..2394..2612...954..3956..5136
.6...76933.21068.26181.25090.17601..3675..9258.10048.20009..7213.26414.32132
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
NT 52  0  0  0  0  0 52
   52  0  0  0  0  0 52
To limit duplication, only the top left-hand corner 52 and the three zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0, T(2,3) = 0 and T(2,4) = 0.

Links

Crossrefs

Cf. A213106, A213249, A213383, A214037, A214119, A214121, A214122, A214359, A213070.

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

A214601 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 6, n >= 2.

Original entry on oeis.org

68, 70, 70, 418, 472, 479, 470, 524, 452, 2401, 3013, 3312, 3043, 2844, 2375, 13344, 18302, 21307, 18726, 17364, 15275, 21050, 15896, 11148, 68230, 98032, 117197, 98032, 95942, 89083, 117197, 89083, 64506, 335569, 494659, 599448, 482769, 488710, 463257, 577787, 465142, 353704, 600124, 458850, 341918
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 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.......68.....70.....70
.3......418....472....479....470....524....452
.4.....2401...3013...3312...3043...2844...2375
.5....13344..18302..21307..18726..17364..15275..21050..15896..11148
.6....68230..98032.117197..98032..95942..89083.117197..89083..64506
.7...335569.494659.599448.482769.488710.463257.577787.465142.353704.600124.458850.341918
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 10 11
NT 68 70 70 70 70 68
   68 70 70 70 70 68
To limit duplication, only the top left-hand corner 68 and the two 70's to its right are stored in the sequence,
i.e. T(2,1) = 68, T(2,2) = 70 and T(2,3) = 70.

Links

Crossrefs

Cf. A213106, A213249, A213379, A214025, A213070, A214397, A214399, A214504, A214510, A214563

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

A214376 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 9, n >= 2.

Original entry on oeis.org

141, 0, 0, 0, 0, 1577, 247, 250, 206, 184, 14, 0, 0, 0, 0, 12996, 3061, 4080, 3938, 3744, 744, 206, 1502, 2186, 2196, 134159, 35481, 51391, 54213, 53870, 19468, 4934, 19662, 27966, 28436, 22132, 8396, 42588, 54710, 52792
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 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......141.....0.....0.....0.....0
.3.....1577...247...250...206...184....14.....0.....0.....0.....0
.4....12996..3061..4080..3938..3744...744...206..1502..2186..2196
.5...134159.35481.51391.54213.53870.19468..4934.19662.27966.28436.22132..8396.42588.54710.52792
where k indicates the position of the end 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 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  16  17
NT 141   0   0   0   0   0   0   0 141
   141   0   0   0   0   0   0   0 141
To limit duplication, only the top left-hand corner 141 and the four zeros to its right are stored in the sequence, i.e. T(2,1) = 141, T(2,2) = 0, T(2,3) = 0, T(2,4) = 0 and T(2,5) = 0.

Links

Crossrefs

Cf. A213106, A213249, A213426, A214042, A214119, A214121, A214122, A214359, A213070, A214373, A214375.

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012
Showing 1-4 of 4 results.

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