cp's OEIS Frontend

A046698 a(0) = 0, a(1) = 1, a(n) = a(a(n-1)) + a(a(n-2)) if n > 1.

%I A046698 #39 Feb 16 2025 08:32:39
%S A046698 0,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A046698 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A046698 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A046698 a(0) = 0, a(1) = 1, a(n) = a(a(n-1)) + a(a(n-2)) if n > 1.
%C A046698 Partial sums are A004275. Binomial transform is A048492, starting with 0. - _Paul Barry_, Feb 28 2003
%C A046698 From _Elmo R. Oliveira_, Jul 25 2024: (Start)
%C A046698 Continued fraction expansion of 2 - sqrt(2) = A101465.
%C A046698 Decimal expansion of 101/9000. (End)
%D A046698 Sequence proposed by Reg Allenby.
%H A046698 Ömür Deveci, Zafer Adıgüzel, and Taha Doğan, <a href="https://doi.org/10.7546/nntdm.2020.26.1.179-190">On the Generalized Fibonacci-circulant-Hurwitz numbers</a>, Notes on Number Theory and Discrete Mathematics (2020) Vol. 26, No. 1, 179-190.
%H A046698 O. Deveci, Y. Akuzum, E. Karaduman, and O. Erdag, <a href="http://dx.doi.org/10.5539/jmr.v7n2p34">The Cyclic Groups via Bezout Matrices</a>, Journal of Mathematics Research, Vol. 7, No. 2, 2015, pp. 34-41.
%H A046698 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>
%H A046698 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A046698 G.f.: x*(1+x^2)/(1-x). - _Paul Barry_, Feb 28 2003
%F A046698 From _Elmo R. Oliveira_, Jul 25 2024: (Start)
%F A046698 E.g.f.: 2*exp(x) - x - 1.
%F A046698 a(n) = 2 for n > 2.
%F A046698 a(n) = 2 - A033324(n+2) = 4 - A343461(n+4) = A114955(n+6) - 6. (End)
%t A046698 CoefficientList[Series[x (1 + x^2)/(1 - x), {x, 0, 104}], x] (* or *)
%t A046698 Nest[Append[#, #[[#[[-1]] + 1]] + #[[#[[-2]] + 1 ]]] &, {0, 1}, 105] (* _Michael De Vlieger_, Jul 31 2020 *)
%o A046698 (PARI) a(n)=(n>0)+(n>2)
%Y A046698 Cf. A004275, A048492, A101465 (decimal expansion of 2 - sqrt(2)).
%Y A046698 Cf. A033324, A114955, A343461.
%K A046698 nonn,easy
%O A046698 0,4
%A A046698 _N. J. A. Sloane_, _R. K. Guy_