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A337188 a(n) = determinant([a(n-1), a(n-2); a(n-4), a(n-3)]) for n >= 5, a(n) = n otherwise.

%I A337188 #32 Oct 23 2022 13:24:59
%S A337188 1,2,3,4,5,7,13,37,194,2263,81209,15670815,35447299799,
%T A337188 2878604306322646,45110072663945746399499,
%U A337188 1599030269628449375351280360624211,4602975420092714513333476912306224941820648781605
%N A337188 a(n) = determinant([a(n-1), a(n-2); a(n-4), a(n-3)]) for n >= 5, a(n) = n otherwise.
%D A337188 B. Muslu, Sayılar ve Bağlantılar, Luna, 2021, pp. 18-22.
%F A337188 a(n) = a(n-1)*a(n-3) - a(n-2)*a(n-4) for n >= 5, a(n) = n for n <= 4.
%p A337188 a:= proc(n) option remember; `if`(n<5, n,
%p A337188       a(n-1)*a(n-3)-a(n-2)*a(n-4))
%p A337188     end:
%p A337188 seq(a(n), n=1..18);  # _Alois P. Heinz_, Jan 29 2021
%t A337188 a[n_] := a[n] = If[n < 5, n, Det @ Map[a, n - {{1, 2}, {4, 3}}, {2}]]; Array[a, 20] (* _Amiram Eldar_, Jan 29 2021 *)
%t A337188 nxt[{a_,b_,c_,d_}]:={b,c,d,Det[{{d,c},{a,b}}]}; NestList[nxt,{1,2,3,4},20][[All,1]] (* _Harvey P. Dale_, Oct 23 2022 *)
%o A337188 (PARI) a(n) = if (n<=4, n, a(n-1)*a(n-3) - a(n-2)*a(n-4)); \\ _Michel Marcus_, Jan 29 2021
%K A337188 nonn
%O A337188 1,2
%A A337188 _Burak Muslu_, Jan 29 2021