A122590 a(n) = 2*a(n-1) - a(n-2) - (a(n-1)^2 + a(n-2)^2).

1, 1, -1, -5, -35, -1315, -1733045, -3003450166025, -9020712899804610407871655, -81373261220701303171562403760549780420204382316935

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..14

Formula

a(n) = 2*a(n-1) - a(n-2) - (a(n-1)^2 + a(n-2)^2), with a(1) = a(2) = 1.

Mathematica

a[n_]:= a[n]= If[n<3, 1, 2*a[n-1] -a[n-2] -(a[n-1]^2 +a[n-2]^2)];
Table[a[n], {n, 0, 10}]
nxt[{a_, b_}] := {b, 2 b - a - (b^2 + a^2)}; NestList[nxt, {1, 1}, 10][[All, 1]] (* Harvey P. Dale, Aug 15 2021 *)

Prog

(Magma)
function a(n) // a = A122590
  if n lt 3 then return 1;
  else return 2*a(n-1) -a(n-2) -(a(n-1)^2 +a(n-2)^2);
  end if; return a;
end function;
[a(n): n in [1..12]]; // G. C. Greubel, Nov 29 2021
(Sage) #a = A122590
def a(n): return 1 if (n<3) else 2*a(n-1) -a(n-2) -(a(n-1)^2 +a(n-2)^2)
[a(n) for n in (1..12)] # G. C. Greubel, Nov 29 2021

Crossrefs

Cf. A122591, A122592, A122593.

Sequence in context: A053420 A321605 A001802 * A057991 A000871 A263882

Adjacent sequences: A122587 A122588 A122589 * A122591 A122592 A122593

Keyword

sign

Author

Roger L. Bagula, Sep 19 2006

Extensions

Edited by N. J. A. Sloane, Sep 21 2006

Status

approved