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 A177238 Number of n-step self-avoiding walks on square lattice plus number of n-step self-avoiding walks on hexagonal [ =triangular ] lattice. 0

%I

%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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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)