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 A214399 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 2, n >= 2. 7
 6, 12, 14, 23, 24, 40, 42, 40, 68, 70, 70, 113, 116, 116, 122, 186, 190, 192, 202, 304, 310, 314, 334, 334, 495, 504, 512, 546, 552, 804, 818, 832, 890, 902, 912, 1304, 1326, 1350, 1446, 1470, 1490, 2113, 2148, 2188, 2346, 2388, 2428, 2434, 3422, 3478, 3544, 3802, 3874, 3944, 3966 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 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 1 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......6 ..3.....12...14 ..4.....23...24 ..5.....40...42...40 ..6.....68...70...70 ..7....113..116..116..122 ..8....186..190..192..202 ..9....304..310..314..334..334 .10....495..504..512..546..552 .11....804..818..832..890..902..912 .12...1304.1326.1350.1446.1470.1490 .13...2113.2148.2188.2346.2388.2428.2434 .14...3422.3478.3544.3802.3874.3944.3966 .15...5540.5630.5738.6158.6278.6398.6442.6462 where k indicates the position of a node in the quarter-rectangle. For each n, the maximum value of k is floor((n+1)/2). Reading this array by rows gives the sequence. LINKS EXAMPLE 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 NT 6 6    6 6 To limit duplication, only the top left-hand corner 6 is stored in the sequence, i.e. T(2,1) = 6. CROSSREFS Cf. A213106, A213249, A213274, A213478, A214119, A214397. Sequence in context: A315612 A315613 A246590 * A079946 A315614 A118586 Adjacent sequences:  A214396 A214397 A214398 * A214400 A214401 A214402 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jul 15 2012 EXTENSIONS Corrected by Christopher Hunt Gribble, Jul 19 2012 STATUS approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)