The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A340005 Number of self-avoiding paths along the edges of a grid with n X n square cells, which do not pass above the diagonal. The paths start at the lower left corner and finish at the upper right corner. 3
 1, 1, 2, 7, 40, 369, 5680, 150707, 6993712, 567670347, 80294818098, 19750798800833, 8447500756620198, 6286515496550185699, 8145835634791919637646, 18387066260739625200447575, 72319765957232441125506763756, 495718308213370458738098777141317 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Siqi Wang, Table of n, a(n) for n = 0..31 EXAMPLE 3 X 3 square cells *---*---*---E | | | | *---*---*---* | | | | *---*---*---* | | | | S---*---*---* a(3) = A000108(3) + 2 = 7; E E E | | | * * *---* | | | * *---*---* *---* | | | S---*---*---* S---* S---* E E | | * *---* | | *---* * | | S---*---* S---*---* E E | | * *---* | | *---* * *---* | | | | S---* *---* S---*---*---* PROG (Python) # Using graphillion from graphillion import GraphSet def make_stairs(n): s = 1 grids = [] for i in range(n + 1, 1, -1): for j in range(i - 1): a, b, c = s + j, s + j + 1, s + i + j grids.extend([(a, b), (a, c)]) s += i return grids def A340005(n): if n == 0: return 1 universe = make_stairs(n) GraphSet.set_universe(universe) start, goal = n + 1, (n + 1) * (n + 2) // 2 paths = GraphSet.paths(start, goal) return paths.len() print([A340005(n) for n in range(15)]) CROSSREFS Row sum of A340043. Cf. A000108, A007764. Sequence in context: A006455 A130715 A317723 * A325061 A358745 A215207 Adjacent sequences: A340002 A340003 A340004 * A340006 A340007 A340008 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 26 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 4 22:06 EDT 2024. Contains 374934 sequences. (Running on oeis4.)