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

1, 2, 3, 4, 5, 7, 13, 37, 194, 2263, 81209, 15670815, 35447299799, 2878604306322646, 45110072663945746399499, 1599030269628449375351280360624211, 4602975420092714513333476912306224941820648781605

Offset: 1

Author

Burak Muslu, Jan 29 2021

Keywords

• nonn

References

• B. Muslu, Sayılar ve Bağlantılar, Luna, 2021, pp. 18-22.

Programs

Maple

a:= proc(n) option remember; `if`(n<5, n,
      a(n-1)*a(n-3)-a(n-2)*a(n-4))
    end:
seq(a(n), n=1..18);  # Alois P. Heinz, Jan 29 2021

Mathematica

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 *)
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 *)

PARI

a(n) = if (n<=4, n, a(n-1)*a(n-3) - a(n-2)*a(n-4)); \\ Michel Marcus, Jan 29 2021

Formula

a(n) = a(n-1)*a(n-3) - a(n-2)*a(n-4) for n >= 5, a(n) = n for n <= 4.