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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 (list; table; graph; refs; listen; history; text; internal format)
 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. LINKS 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 Adjacent sequences: A213246 A213247 A213248 * A213250 A213251 A213252 KEYWORD nonn,tabl AUTHOR Christopher Hunt Gribble, Jun 07 2012 STATUS approved

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Last modified January 28 22:08 EST 2023. Contains 359905 sequences. (Running on oeis4.)