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.

A214503 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 7, n >= 2.

Original entry on oeis.org

113, 116, 116, 122, 906, 1028, 1050, 1088, 1016, 1152, 1020, 980, 6751, 8562, 9411, 9718, 8651, 8317, 7116, 6882, 50036, 69029, 80263, 82942, 71736, 67670, 61229, 60116, 81276, 63148, 46550, 44196, 335569, 482769, 577787, 600124, 494659, 488710, 465142, 458850, 599448, 463257, 353704, 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 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......113....116....116....122
.3......906...1028...1050...1088...1016...1152...1020....980
.4.....6751...8562...9411...9718...8651...8317...7116...6882
.5....50036..69029..80263..82942..71736..67670..61229..60116..81276..63148..46550..44196
.6...335569.482769.577787.600124.494659.488710.465142.458850.599448.463257.353704.341918
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
NT 113 116 116 122 116 116 113
   113 116 116 122 116 116 113
To limit duplication, only the top left-hand corner 113 and the 116, 116, 122 to its right are stored in the sequence,
i.e. T(2,1) = 113, T(2,2) = 116, T(2,3) = 116 and T(2,4) = 122.

Links

Crossrefs

Cf. A213106, A213249, A213383, A214037, A214373, A214397, A214399, A214504, A214510, A214563, A214601

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

A214608 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 9, n >= 2.

Original entry on oeis.org

304, 310, 314, 334, 334, 4137, 4754, 4811, 4929, 4920, 4610, 5260, 4738, 4784, 4924, 50775, 66474, 72137, 71469, 69764, 65977, 63790, 55400, 55907, 57274, 676474, 969677, 1118226, 1096104, 1058044, 1003962, 946620, 864012, 870946, 884912, 1154902, 887242, 651592, 669896, 710904
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 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......304.....310.....314.....334.....334
.3.....4137....4754....4811....4929....4920....4610....5260....4738....4784....4924
.4....50775...66474...72137...71469...69764...65977...63790...55400...55907...57274
.5...676474..969677.1118226.1096104.1058044.1003962..946620..864012..870946..884912.1154902..887242..651592..669896..710904
where k indicates the position of a 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 (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  16  17
NT 304 310 314 334 334 334 314 310 304
   304 310 314 334 334 334 314 310 304
To limit duplication, only the top left-hand corner 304 and the 310, 314, 334, 334 to its right are stored in the sequence,
i.e. T(2,1) = 304, T(2,2) = 310, T(2,3) = 314, T(2,4) = 334 and T(2,5) = 334.

Links

Crossrefs

Cf. A213106, A213249, A213426, A214042, A214376, A214397, A214399, A214504, A214510, A214563, A214601, A214503, A214605
Showing 1-3 of 3 results.

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