A000283 a(n) = a(n-1)^2 + a(n-2)^2 for n >= 2 with a(0) = 0 and a(1) = 1.

0, 1, 1, 2, 5, 29, 866, 750797, 563696885165, 317754178345286893212434, 100967717855888389973004846476977145423449281581

Offset: 0

Author

Stephen J. Greenfield (greenfie(AT)math.rutgers.edu)

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..14
• Steven J. Miller (ed.), Benford's Law: Theory and Applications, Princeton University Press, 2015; see page 5.

Crossrefs

Cf. A000278.

Programs

Maple

A000283 := proc(n) option remember; if n <= 1 then n else A000283(n-2)^2+A000283(n-1)^2; fi; end;

Mathematica

RecurrenceTable[{a[n + 2] == a[n + 1]^2 + a[n]^2, a[0] == 0, a[1] == 1}, a, {n, 0, 12}] (* Emanuele Munarini, Mar 30 2017 *)

Maxima

a(n) := if n=0 then 0 elseif n=1 then 1 else a(n-1)^2 + a(n-2)^2;
makelist(a(n),n,0,12); /* Emanuele Munarini, Mar 30 2017 */

PARI

{a(n) = if( n<2, n>0, a(n-1)^2 + a(n-2)^2)}; /* Michael Somos, Feb 10 2002 */

Formula

a(0)=0; for n >= 1, a(n) = floor(A^(2^(n-1))), where A=1.2353927377854368896\ 22331013228440824347457186913679454733601897236639743839118542826528455451978134... - Benoit Cloitre, May 03 2003

Extensions

Name clarified by David A. Corneth, Jul 14 2018