|
Search: id:A000278
|
|
|
| A000278 |
|
a(n) = a(n-1) + a(n-2)^2. |
|
+0
11
|
|
| 0, 1, 1, 2, 3, 7, 16, 65, 321, 4546, 107587, 20773703, 11595736272, 431558332068481, 134461531248108526465, 186242594112190847520182173826
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
LINKS
|
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 (benoit7848c(AT)orange.fr), 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); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2009]
|
|
PROGRAM
|
(PARI) a(n)=if(n<2, n>0, a(n-1)+a(n-2)^2)
|
|
CROSSREFS
|
Cf. A000283.
Sequence in context: A002854 A036356 A034732 this_sequence A153787 A141795 A077322
Adjacent sequences: A000275 A000276 A000277 this_sequence A000279 A000280 A000281
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
greenfie(AT)math.rutgers.edu (Stephen J. Greenfield)
|
|
|
Search completed in 0.002 seconds
|
