cp's OEIS Frontend

A177238 Number of n-step self-avoiding walks on square lattice plus number of n-step self-avoiding walks on hexagonal [ =triangular ] lattice.

%I A177238 #12 Mar 30 2012 18:40:52
%S A177238 2,10,42,174,718,3014,12726,54054,230046,980402,4177266,17789230,
%T A177238 75680138,321616186,1365165694,5788182178,24514575654,103720434558,
%U A177238 438421398326,1851566492994,7813337317842,32946701361962,138832416613530
%N A177238 Number of n-step self-avoiding walks on square lattice plus number of n-step self-avoiding walks on hexagonal [ =triangular ] lattice.
%C A177238 a(0) = 2 is the only prime in the sequence. (By symmetry in both lattices, we are adding two sequences with even terms if n>0.)  a(n) is semiprime for a(1) = 10 = 2 * 5, a(4) = 718 = 2 * 359, a(9) = 980402 = 2 * 490201. The Jensen table linked from A001334 should allow extension through a(40).
%F A177238 a(n) = A001334(n) + A001411(n).
%e A177238 n\Triangle | Square | Sum
%e A177238 0          1     1     2
%e A177238 1          6     4     10
%e A177238 2          30    12    42
%e A177238 3          138   36    174
%e A177238 4          618   100   718
%e A177238 5          2730  284   3014
%e A177238 6          11946 780   12726
%Y A177238 Cf. A001334, A001411.
%K A177238 nonn,walk
%O A177238 0,1
%A A177238 _Jonathan Vos Post_, Dec 11 2010