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A000278 a(n) = a(n-1) + a(n-2)^2. 15
0, 1, 1, 2, 3, 7, 16, 65, 321, 4546, 107587, 20773703, 11595736272, 431558332068481, 134461531248108526465, 186242594112190847520182173826, 18079903385772308300945867582153787570051, 34686303861638264961101080464895364211215702792496667048327 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

T. D. Noe, Table of n, a(n) for n = 0..25

W. Duke, Stephen J. Greenfield and Eugene R. Speer, Properties of a Quadratic Fibonacci Recurrence, J. Integer Sequences, 1998, #98.1.8.

FORMULA

a(2n) is asymptotic to A^(sqrt(2)^(2n-1)) where A=1.668751581493687393311628852632911281060730869124873165099170786836201970866312366402366761987... and a(2n+1) to B^(sqrt(2)^(2n)) where B=1.693060557587684004961387955790151505861127759176717820241560622552858106116817244440438308887... See reference for proof. - Benoit Cloitre, May 03 2003

MAPLE

A000278 := proc(n) option remember; if n <= 1 then n else A000278(n-2)^2+A000278(n-1); fi; end;

a[ -2]:=0: a[ -1]:=1:a[0]:=1: a[1]:=2: for n from 2 to 13 do a[n]:=a[n-1]+a[n-2]^2 od: seq(a[n], n=-2..13); # Zerinvary Lajos, Mar 19 2009

MATHEMATICA

Join[{a=0, b=1}, Table[c=a^2+b; a=b; b=c, {n, 16}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *)

RecurrenceTable[{a[n +2] == a[n +1] + a[n]^2, a[0] == 1, a[1] == 1}, a, {n, 0, 16}] (* Robert G. Wilson v, Apr 14 2017 *)

PROG

(PARI) a(n)=if(n<2, n>0, a(n-1)+a(n-2)^2)

(Sage)

def A000278():

    x, y = 0, 1

    while true:

        yield x

        x, y = x + y, x * x

a = A000278(); [a.next() for i in range(18)]  # Peter Luschny, Dec 17 2015

(MAGMA) [n le 2 select n-1 else Self(n-1) + Self(n-2)^2: n in [1..18]]; // Vincenzo Librandi, Dec 17 2015

CROSSREFS

Cf. A000283, A058182.

Sequence in context: A002854 A036356 A034732 * A270525 A153787 A141795

Adjacent sequences:  A000275 A000276 A000277 * A000279 A000280 A000281

KEYWORD

nonn,changed

AUTHOR

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

STATUS

approved

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Last modified April 28 00:42 EDT 2017. Contains 285555 sequences.