|
%I #18 Jun 23 2022 19:13:13
%S 3,5,9,13,23,35,59,93,153,245,399,643,1043,1685,2729,4413,7143,11555,
%T 18699,30253,48953,79205,128159,207363,335523,542885,878409,1421293,
%U 2299703,3720995,6020699,9741693,15762393,25504085,41266479,66770563
%N a(n) = A014217(n+3) - A014217(n).
%C The least significant digits are a sequence of period length 4: 3,5,9,3.
%C One could extend A014217 using its recurrence to define A014217(-1)=-1. This would add a(-1)=3 here by definition, and the least significant digits would still follow the (same, wrapped) period of length 4: 3,3,5,9.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,1).
%F a(2n+2) = a(2n+1) + a(2n) + 1. a(2n+3) = a(2n+2) + a(2n+1) - 1.
%F From _R. J. Mathar_, Feb 07 2009, Apr 18 2009: (Start)
%F a(n) = 2*a(n-2) + a(n-3) = (-1)^n + 2*A000032(n+1).
%F G.f.: (3+5x+3x^2)/ ((1+x)(1-x-x^2)). (End)
%F a(n) + a(n+1) = A022112(n+2). - _R. J. Mathar_, Feb 25 2013
%F a(n) = ((-2)^n + (1 - sqrt(5))^(1+n) + (1 + sqrt(5))^(1+n))/2^n. - _Stefano Spezia_, Dec 25 2021
%t LinearRecurrence[{0,2,1},{3,5,9},40] (* _Harvey P. Dale_, Jun 23 2022 *)
%Y Cf. A022112.
%K nonn,easy
%O 0,1
%A _Paul Curtz_, Dec 22 2008
%E More terms from _R. J. Mathar_, Feb 07 2009
%E Edited by _R. J. Mathar_, Apr 18 2009
|
