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

Author

Francois Alcover, May 05 2016

Keywords

• nonn
• walk

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

Crossrefs

Cf. A272265.

Formula

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