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%I #12 Mar 30 2012 18:40:52
%S 2,10,42,174,718,3014,12726,54054,230046,980402,4177266,17789230,
%T 75680138,321616186,1365165694,5788182178,24514575654,103720434558,
%U 438421398326,1851566492994,7813337317842,32946701361962,138832416613530
%N Number of n-step self-avoiding walks on square lattice plus number of n-step self-avoiding walks on hexagonal [ =triangular ] lattice.
%C 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 a(n) = A001334(n) + A001411(n).
%e n\Triangle | Square | Sum
%e 0 1 1 2
%e 1 6 4 10
%e 2 30 12 42
%e 3 138 36 174
%e 4 618 100 718
%e 5 2730 284 3014
%e 6 11946 780 12726
%Y Cf. A001334, A001411.
%K nonn,walk
%O 0,1
%A _Jonathan Vos Post_, Dec 11 2010
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