This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058182 a(n) = a(n-1)^2 + a(n-2), a(0)=1, a(1)=0. 8
 1, 0, 1, 1, 2, 5, 27, 734, 538783, 290287121823, 84266613096281243382112, 7100862082718357559748563880517486086728702367, 50422242317787290639189291009890702507917377925161079229314384058371278254659634544914784801 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Has property that CONTINUANT([1, 1, 2, 5, 27, 734, 538783, ...]) = [1, 2, 5, 27, 734, 538783, ...]. - N. J. A. Sloane Jul 19 2002 For n > 2, a(n) is the numerator of the simplified continued fraction resulting from [a(2), a(3), ..., a(n)]. Therefore, for n > 2, a(n) represents the number of ways to tile a (n-2)-board with dominoes and stackable squares, where nothing can be stacked on a domino but otherwise for 2 < i < n, the i-th cell may be stacked by as many as a(i) squares (see Benjamin, A. and Quinn, J.). - Melvin Peralta, Feb 22 2016 REFERENCES Arthur Benjamin and Jennifer Quinn, Proofs that Really Count, Mathematical Association of America, 2003, see pages 49-51. LINKS Melvin Peralta, Table of n, a(n) for n = 0..15 N. J. A. Sloane, Transforms FORMULA a(n)^2 = a(n+1) - a(n-1), a(-1-n) = -a(n). For n > 1, a(n+1) = floor(c^(2^n)) where c=1.108604586393628626769904017539.... - Benoit Cloitre, Nov 30 2002 a(n+1) = a(n)^2 + floor(sqrt(a(n))) = A000290(a(n)) + A000196(a(n)) for n > 2. - Reinhard Zumkeller, May 16 2006 EXAMPLE a(6) = a(5)^2 + a(4) = 5^2 + 2 = 27. MATHEMATICA Join[{a=1, b=0}, Table[c=a+b^2; a=b; b=c, {n, 12}]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2011 *) Join[{1}, Transpose[NestList[{Last[#], Last[#]^2+First[#]}&, {0, 1}, 12]][[1]]] (* Harvey P. Dale, May 15 2011 *) RecurrenceTable[{a[0] == 1, a[1] == 0, a[n] == a[n-1]^2 + a[n-2]}, a, {n, 13}] (* Vincenzo Librandi, Feb 23 2016 *) PROG (PARI) a(n)=if(n<0, -a(-1-n), if(n<2, 1-n, a(n-1)^2+a(n-2))) /* Michael Somos, May 05 2005 */ (MAGMA) I:=[1, 0]; [n le 2 select I[n] else Self(n-1)^2+Self(n-2): n in [1..13]]; // Vincenzo Librandi, Feb 23 2016 CROSSREFS Cf. A000278, A005605, A058181. Sequence in context: A079716 A322151 A203195 * A057438 A002795 A208218 Adjacent sequences:  A058179 A058180 A058181 * A058183 A058184 A058185 KEYWORD nonn,nice,eigen AUTHOR Henry Bottomley, Nov 15 2000 EXTENSIONS More terms from Reinhard Zumkeller, May 16 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 12:22 EDT 2019. Contains 328026 sequences. (Running on oeis4.)