A214375 -id:A214375 - cp's OEIS frontend

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.

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

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

Christopher Hunt Gribble, Jul 22 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......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.

			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.

Cf. A213106, A213249, A213425, A214038, A214375, A214397, A214399, A214504, A214510, A214563, A214601, A214503

cp's OEIS Frontend

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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