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A368129 A variant of A367146 with application of the distance minimization to the second of two symmetrized versions of the strip bijection between two square lattices as described in A368126.

%I A368129 #8 Jan 06 2024 23:00:19
%S A368129 1,8,12,24,72,156,168,216,264,624,1560,1752,1836,2232,4824,12456,
%T A368129 13080,16380,17064,35040,92184,92952,123096,128844,244584,639192,
%U A368129 651432,855240,945756
%N A368129 A variant of A367146 with application of the distance minimization to the second of two symmetrized versions of the strip bijection between two square lattices as described in A368126.
%C A368129 Apparently, a(n) == 0 (mod 4) for n > 1. For cycles, whose lengths are multiples of 8, the visited points form 8 separated islands.
%C A368129 Larger terms are 1660752, 4293336, 4462104, 5787768, 6647916, 11050488, 28333080, 38414184, 45366204, 184427544.
%H A368129 Hugo Pfoertner, <a href="/A368129/a368129.png">Example of one of the 8 islands in orbit with L=184427544</a>.
%e A368129 See files linked in A368130 for visualization of orbits.
%o A368129 (PARI) \\ Uses definitions and functions from
%o A368129 \\ a367150_PARI.txt and a368126_PARI.txt
%o A368129 cycle(v) = {my (n=1, w=BijectionD(v, Bijectionk)); while (w!=v, n++; w=BijectionD(w, Bijectionk)); n};
%o A368129 a368129(rmax=235) = {my (L=List()); for (r2=0, rmax^2, for (x=0, sqrtint(r2), my (y2=r2-x^2, y); if (issquare(y2, &y), if(x>=y, my (c=cycle([x, y])); if (setsearch(L, c)==0, print([c, [x, y], sqrt(x^2+y^2)], ", "); listput(L, c); listsort(L, 1)))))); L};
%o A368129 a368129() \\ Terms < 1000, takes 5-10 minutes CPU time
%Y A368129 Cf. A307110, A367146, A367150, A368126.
%Y A368129 A368130 is a permutation of this sequence.
%Y A368129 A368124 is the analog for the first symmetrized version of the strip bijection.
%K A368129 nonn,more
%O A368129 1,2
%A A368129 _Hugo Pfoertner_, Jan 03 2024