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%I #32 Apr 03 2020 15:36:53
%S 1,10,7056,462755440,2593165016903538,1243982213040307428318660,
%T 51166088445891978924432033203830714,
%U 180349587397776823066172713933745722978533730900
%N "Crossing walks hitting the center" on the square lattice (see Jensen web site for further information).
%H I. Jensen, <a href="/A121787/b121787.txt">Table of n, a(n) for n = 0..9</a> [from the Jensen link below; a(0)=1 prepended by _Georg Fischer_, Apr 03 2020]
%H I. Jensen, <a href="https://web.archive.org/web/20160102102505/http://www.ms.unimelb.edu.au/~iwan/saw/SAW_ser.html">Series Expansions for Self-Avoiding Walks</a> [Wayback Machine]
%F a(n) = A333685(n,n). - _Seiichi Manyama_, Apr 02 2020
%e From _Seiichi Manyama_, Apr 01 2020: (Start)
%e a(1) = 10;
%e S--*--* S--*--* S--* S--* S--*
%e | | | | |
%e +--* *--+--* +--* + *--+
%e | | | | |
%e *--E *--*--E E *--E *--*--E
%e S *--* S *--* S S S
%e | | | | | | | | |
%e * + * *--+ * * +--* *--+--* *--+
%e | | | | | | | | |
%e *--* E E *--* E E *--E
%e a(2) = 7056;
%e S--*--*--*--* S--*--*--*--* S--*--*--*--*
%e | | |
%e *--*--*--*--* *--*--*--*--* *--*--*--*--*
%e | | |
%e *--*--+ *--*--+ *--*--+
%e | | |
%e *--*--* *--* *--* *--*
%e | | | | |
%e *--*--*--*--E *--*--* E *--*--*--E
%e ... and so on.
%e (End)
%o (Python)
%o # Using graphillion
%o from graphillion import GraphSet
%o import graphillion.tutorial as tl
%o def A121787(n):
%o if n == 0: return 1
%o universe = tl.grid(2 * n, 2 * n)
%o GraphSet.set_universe(universe)
%o start, goal = 1, (2 * n + 1) * (2 * n + 1)
%o paths = GraphSet.paths(start, goal).including((start + goal) // 2)
%o return paths.len()
%o print([A121787(n) for n in range(7)]) # _Seiichi Manyama_, Apr 01 2020
%Y Cf. A333674, A333685.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Aug 30 2006
%E a(0)=1 prepended by _Seiichi Manyama_, Apr 02 2020
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