A122592 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, 2, 4, 4, 2, 6, 18, 144, 15882, 247684656, 61339821614663208, 3762573685332838515711641628032454, 14156960737559137644661747812427568488753428461913274274176986277422

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..19

Formula

a(n) = a(n-1) - 2*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

(* First program *)
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, 20}]
(* Second program *)
RecurrenceTable[{a[1]==a[2]==a[3]==1, a[n]==-a[n-1]+a[n-3]+(a[n-2]-a[n-1])^2+(a[n-2]-a[n-3])^2}, a, {n, 20}] (* Harvey P. Dale, Dec 18 2012 *)

Prog

(Magma)
function a(n) // a = A122592
  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..18]]; // 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 = A122592
[a(n) for n in (1..18)] # G. C. Greubel, Nov 29 2021

Crossrefs

Cf. A122590, A122591, A122593.

Sequence in context: A206389 A206503 A323938 * A099264 A011172 A193028

Adjacent sequences: A122589 A122590 A122591 * A122593 A122594 A122595

Keyword

nonn

Author

Roger L. Bagula, Sep 19 2006

Extensions

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

Definition corrected by Harvey P. Dale, Dec 18 2012

Status

approved