A272480 Number of n-step tri-directional self-avoiding walks on the hexagonal lattice, after first step.

3, 7, 17, 41, 95, 223, 523, 1201, 2781, 6445, 14731, 33859, 77899, 177523, 406115, 929825, 2114387, 4821367, 11001423, 24974353, 56813401, 129315249, 293157759, 665688917, 1512325105, 3424615395

Offset

1,1

Comments

Among the 6 possible directions only 3 are allowed, separated by 120 degrees.

We take a first step then count all the n-step walks.

This sequence generates a surprising number of primes:

* 3: 3

* 7: 7

* 17: 17

* 41: 41

95: 5 19

* 223: 223

* 523: 523

* 1201: 1201

2781: 3 3 3 103

6445: 5 1289

* 14731: 14731

33859: 7 7 691

* 77899: 77899

177523: 113 1571

406115: 5 81223

929825: 5 5 13 2861

2114387: 11 167 1151

4821367: 1229 3923

11001423: 3 3667141

* 24974353: 24974353

56813401: 19 59 59 859

129315249: 3 3 7 101 20323

293157759: 3 97719253

665688917: 59 11282863

1512325105: 5 523 578327

3424615395: 3 5 12497 18269

Links

Table of n, a(n) for n=1..26.

Formula

a(n) = A272265(n)/3.

Crossrefs

Cf. A272265.

Sequence in context: A000600 A138901 A192674 * A131056 A077851 A089737

Adjacent sequences: A272477 A272478 A272479 * A272481 A272482 A272483

Keyword

nonn,walk

Author

Francois Alcover, May 05 2016

Status

approved