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a(n) is the numerator of the probability that a self-avoiding random walk on the cubic lattice is trapped after n steps.
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%I #10 Oct 21 2024 09:00:06

%S 8,38,637,9759,86221819,28522360751,583791967829,1801511107253,

%T 6467456149881773

%N a(n) is the numerator of the probability that a self-avoiding random walk on the cubic lattice is trapped after n steps.

%H <a href="/plot2a?name1=A377161&amp;name2=A377162&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=ratio&amp;drawpoints=true">Plot of a(n)/A377162(n) vs n</a>, using Plot 2.

%F a(n)/A377162(n) = A077818(n) / (5^(n-1) * 3^A077819(n) * 2^A077820(n)).

%e 8/1953125, 38/9765625, 637/58593750, 9759/976562500, 86221819/4687500000000, 28522360751/1687500000000000, 583791967829/22500000000000000, ...

%Y A377162 are the corresponding denominators.

%Y Cf. A001412, A077817, A077818 (see there for more information), A077819, A077820.

%K nonn,frac,walk,hard,more

%O 11,1

%A _Hugo Pfoertner_, Oct 20 2024