A122593 a(n) = -a(n-1) + a(n-3) - (a(n-1) - a(n-2))^2 + (a(n-2) - a(n-3))^2.

1, 1, 1, 0, 0, 2, -6, -54, -2184, -4532418, -20523011025492, -421193795514716517978851412, -177404213380075544048510970681865493733941889439557930

Offset

1,6

Links

G. C. Greubel, Table of n, a(n) for n = 1..17

Formula

a(n) = -a(n-1) + a(n-3) - (a(n-1) - a(n-2))^2 + (a(n-2) - a(n-3))^2, with a(1) = a(2) = a(3) = 1.

Mathematica

a[n_]:= a[n]= If[n<4, 1, -a[n-1] +a[n-3] - (a[n-1] -a[n-2])^2 + (a[n-2] -a[n-3])^2];
Table[a[n], {n, 15}]

Prog

(Magma)
function a(n) // a = A122593
  if n lt 4 then return 1;
  else return -a(n-1) +a(n-3) -(a(n-1) -a(n-2))^2 +(a(n-2) -a(n-3))^2;
  end if; return a; end function;
[a(n): n in [1..15]]; // G. C. Greubel, Nov 29 2021
(Sage)
@CachedFunction
def a(n): return 1 if (n<4) else -a(n-1) +a(n-3) -(a(n-1) -a(n-2))^2 +(a(n-2) -a(n-3))^2 # a = A122593
[a(n) for n in (1..15)] # G. C. Greubel, Nov 29 2021

Crossrefs

Cf. A122590, A122591, A122592.

Sequence in context: A152543 A279454 A306021 * A267348 A264610 A153450

Adjacent sequences: A122590 A122591 A122592 * A122594 A122595 A122596

Keyword

sign,changed

Author

Roger L. Bagula, Sep 19 2006

Extensions

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

Recurrence formula corrected by Georg Fischer, Apr 10 2024

Status

approved