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A213249
Triangle T(n,k) of numbers of distinct shapes under rotation of non-extendable (complete) non-self-adjacent simple paths within a square lattice bounded by rectangles with nodal dimensions n and k, n >= k >= 2.
40
2, 8, 16, 18, 64, 134, 34, 170, 706, 1854, 60, 398, 2346, 13198, 41478, 102, 880, 6832, 55454, 382116, 1424988
OFFSET
2,1
COMMENTS
The triangle of numbers is:
....k....2....3.....4......5.......6........7
.n
.2.......2
.3.......8...16
.4......18...64...134
.5......34..170...706...1854
.6......60..398..2346..13198...41478
.7.....102..880..6832..55454..382116..1424988
The sequence is formed by reading the triangle by rows.
FORMULA
Let T(n,k) denote an element of the triangle then the following recurrence relations appear to hold:
T(n, 2) - T(n-1, 2) - 2*A000045(n+1) = 0, n >= 3,
T(n, 3) - 2*T(n-1, 3) - T(n-4, 3) - 4*(n+11) = 0, n >= 7.
EXAMPLE
T(2,2) = The number of rotationally distinct complete non-self-adjacent simple path shapes within a 2 X 2 node rectangle.
CROSSREFS
Cf. A213106.
Sequence in context: A174882 A080095 A193219 * A155853 A256552 A031061
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved