A272265 -id:A272265 - cp's OEIS frontend

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

Francois Alcover, May 05 2016

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

Cf. A272265.

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

cp's OEIS Frontend

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

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