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

2, 10, 42, 174, 718, 3014, 12726, 54054, 230046, 980402, 4177266, 17789230, 75680138, 321616186, 1365165694, 5788182178, 24514575654, 103720434558, 438421398326, 1851566492994, 7813337317842, 32946701361962, 138832416613530

Offset

0,1

Comments

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).

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = A001334(n) + A001411(n).

Example

n\Triangle | Square | Sum
0          1     1     2
1          6     4     10
2          30    12    42
3          138   36    174
4          618   100   718
5          2730  284   3014
6          11946 780   12726

Crossrefs

Cf. A001334, A001411.

Sequence in context: A302524 A084180 A020988 * A084480 A309182 A099553

Adjacent sequences: A177235 A177236 A177237 * A177239 A177240 A177241

Keyword

nonn,walk

Author

Jonathan Vos Post, Dec 11 2010

Status

approved