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A375922 a(n) = (a(n-3)*a(n-9) + a(n-1)*a(n-11))/a(n-12) with a(0) = ... = a(11) = 1.

%I A375922 #37 Feb 16 2025 08:34:07
%S A375922 1,1,1,1,1,1,1,1,1,1,1,1,2,3,4,6,9,13,19,28,41,79,163,490,972,1785,
%T A375922 4270,9483,19251,41603,100739,259579,997371,3297339,12754875,33992883,
%U A375922 94594611,363844867,1139238123,3317604094,12075672425,56552033036,254310500890
%N A375922 a(n) = (a(n-3)*a(n-9) + a(n-1)*a(n-11))/a(n-12) with a(0) = ... = a(11) = 1.
%C A375922 Sequence defined by recursion derived from Sato discrete tau function.
%C A375922 When extended to n<0 by a(n) = a(13-n) for all n in Z, then also a(n+6)*a(n-6) = a(n+5)*a(n-5) + a(n+3)*a(n-3) for all n in Z. It is a Gale-Robinson sequence. - _Michael Somos_, Nov 28 2024
%H A375922 Alois P. Heinz, <a href="/A375922/b375922.txt">Table of n, a(n) for n = 0..345</a>
%H A375922 Mohamed Bensaid, <a href="https://arxiv.org/abs/2409.05911">Sato tau functions and construction of Somos sequence</a>, arXiv:2409.05911 [math.NT], 2024.
%H A375922 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SomosSequence.html">Somos Sequence</a>.
%p A375922 a:= proc(n) option remember; `if`(n<12, 1,
%p A375922      (a(n-3)*a(n-9)+a(n-1)*a(n-11))/a(n-12))
%p A375922     end:
%p A375922 seq(a(n), n=0..42);  # _Alois P. Heinz_, Sep 02 2024
%t A375922 a[n_] := a[n] = If[n < 12, 1, (a[n-3]*a[n-9] + a[n-1]*a[n-11]) / a[n-12]]; Array[a, 40, 0] (* _Amiram Eldar_, Sep 02 2024 *)
%o A375922 (PARI) seq(n)={my(a=vector(n+1,i,1)); for(n=13, #a, a[n] =(a[n-3]*a[n-9]+a[n-1]*a[n-11])/a[n-12]); a} \\ _Andrew Howroyd_, Sep 03 2024
%Y A375922 Cf. A375621.
%K A375922 nonn
%O A375922 0,13
%A A375922 _Mohamed Bensaid_, Sep 02 2024