A214121 -id:A214121 - cp's OEIS frontend

A214122 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 4, n >= 2.

10, 0, 33, 6, 4, 0, 90, 22, 22, 4, 256, 52, 67, 14, 88, 32, 720, 104, 187, 30, 236, 108, 1931, 200, 495, 56, 622, 262, 602, 364, 5029, 386, 1245, 106, 1624, 618, 1537, 898, 12996, 744, 3061, 206, 4080, 1502, 3938, 2186, 3744, 2196, 33512, 1422, 7615, 398

Offset: 2

Christopher Hunt Gribble, Jul 04 2012

The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 2 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
..n
..2......10.....0
..3......33.....6.....4.....0
..4......90....22....22.....4
..5.....256....52....67....14....88....32
..6.....720...104...187....30...236...108
..7....1931...200...495....56...622...262...602...364
..8....5029...386..1245...106..1624...618..1537...898
..9...12996...744..3061...206..4080..1502..3938..2186..3744..2196
.10...33512..1422..7615...398.10014..3676..9775..5466..9177..5246
where k indicates the position of the end node in the quarter-rectangle. For each n, the maximum value of k is 2*floor((n+1)/2). Reading this array by rows gives the sequence.

			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
NT 10  0  0 10
   10  0  0 10
To limit duplication, only the top left-hand corner 10 and the 0 to its right are stored in the sequence, i.e. T(2,1) = 10 and T(2,2) = 0.

Cf. A213106, A213249, A213342, A214022, A214119, A214121.

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

A214504 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 3, n >= 2.

Original entry on oeis.org

12, 14, 32, 36, 36, 48, 80, 88, 86, 100, 188, 210, 209, 228, 204, 204, 418, 470, 472, 524, 479, 452, 906, 1016, 1028, 1152, 1050, 1020, 1088, 980, 1943, 2170, 2219, 2472, 2250, 2222, 2333, 2200, 4137, 4610, 4754, 5260, 4811, 4738, 4929, 4784, 4920, 4924

Offset: 2

Christopher Hunt Gribble, Jul 19 2012

The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 2 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
..n
..2.....12...14
..3.....32...36...36...48
..4.....80...88...86..100
..5....188..210..209..228..204..204
..6....418..470..472..524..479..452
..7....906.1016.1028.1152.1050.1020.1088..980
..8...1943.2170.2219.2472.2250.2222.2333.2200
..9...4137.4610.4754.5260.4811.4738.4929.4784.4920.4924
where k indicates the position of a node in the quarter-rectangle.
For each n, the maximum value of k is 2*floor((n+1)/2).
Reading this array by rows gives the sequence.

			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
NT 12 14 12
   12 14 12
To limit duplication, only the top left-hand corner 12 and the 14 to its right are stored in the sequence,
  i.e. T(2,1) = 12 and T(2,2) = 14.

Cf. A213106, A213249, A213089, A213954, A214121, A214397, A214399

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

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

Christopher Hunt Gribble, Jul 13 2012

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.

			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.

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

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

A213070 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 6, n >= 2.

Original entry on oeis.org

31, 0, 0, 165, 27, 32, 8, 0, 0, 720, 187, 236, 104, 30, 108, 3431, 992, 1179, 746, 251, 580, 920, 352, 1210, 16608, 4361, 5027, 4361, 1094, 2043, 5027, 2043, 6268, 76933, 17601, 20009, 21068, 3675, 7213, 26181, 9258, 26414, 25090, 10048, 32132

Offset: 2

Christopher Hunt Gribble, Jul 13 2012

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......31.....0.....0
.3.....165....27....32.....8.....0.....0
.4.....720...187...236...104....30...108
.5....3431...992..1179...746...251...580...920...352..1210
.6...16608..4361..5027..4361..1094..2043..5027..2043..6268
.7...76933.17601.20009.21068..3675..7213.26181..9258.26414.25090.10048.32132
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.

			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
NT 31  0  0  0  0 31
   31  0  0  0  0 31
To limit duplication, only the top left-hand corner 31 and the two zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0 and T(2,3) = 0.

Cf. A213106, A213249, A213379, A214025, A214119, A214121, A214122, A214359.

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

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

Christopher Hunt Gribble, Jul 14 2012

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.

			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.

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

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

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

Christopher Hunt Gribble, Jul 14 2012

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.

			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.

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

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

Christopher Hunt Gribble, Jul 14 2012

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.

			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.

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

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

cp's OEIS Frontend

A214122 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 4, n >= 2.

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A214504 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 3, n >= 2.

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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.

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A213070 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 6, n >= 2.

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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.

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Extensions

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.

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Extensions

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.

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