cp's OEIS Frontend

A096062 a(1) = a(2) = 1; for n > 2, if a(n-2) + a(n-1) > n then a(n) = abs(a(n-2) - a(n-1)) else a(n) = a(n-2) + a(n-1).

%I A096062 #14 Jun 13 2015 00:51:23
%S A096062 1,1,2,3,5,2,7,5,2,7,9,2,11,13,2,15,17,2,19,17,2,19,21,2,23,25,2,27,
%T A096062 29,2,31,29,2,31,33,2,35,37,2,39,41,2,43,41,2,43,45,2,47,49,2,51,53,2,
%U A096062 55,53,2,55,57,2,59,61,2,63,65,2,67,65,2,67,69,2,71,73,2,75,77,2,79,77,2
%N A096062 a(1) = a(2) = 1; for n > 2, if a(n-2) + a(n-1) > n then a(n) = abs(a(n-2) - a(n-1)) else a(n) = a(n-2) + a(n-1).
%C A096062 For n > 1: a(n) = 2 if n mod 12 = {0,3,6,9}, a(n) = n if n mod 12 = {5,7}, a(n) = n-1 if n mod 12 = {2,4}, a(n) = n-2 if n mod 12 = {1,11}, a(n) = n-3 if n mod 12 = {8,10}. - _Klaus Brockhaus_, Jun 19 2004
%H A096062 Harvey P. Dale, <a href="/A096062/b096062.txt">Table of n, a(n) for n = 1..1000</a>
%H A096062 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,-1,-1,1,1,-1,-1,1,1,0,-1).
%F A096062 G.f.: x*(2*x^13 -2*x^12 +x^11 +5*x^10 -x^9 -x^8 +x^7 +x^6 -x^5 +3*x^4 +x^3 +x^2 +x +1) / ((x -1)^2*(x +1)*(x^2 -x +1)*(x^2 +x +1)^2*(x^4 -x^2 +1)). - _Colin Barker_, Mar 12 2015
%e A096062 a(8) + a(9) = 5 + 2 = 7 < 10, so a(10) = 7.
%e A096062 a(16) + a(17) = 15 + 17 = 32 > 18, so a(18) = abs(15 - 17) = 2.
%t A096062 nxt[{n_,a_,b_}]:={n+1,b,If[a+b>n+1,Abs[a-b],a+b]}; Transpose[ NestList[ nxt,{2,1,1},90]][[2]] (* _Harvey P. Dale_, Sep 22 2014 *)
%o A096062 (PARI) m=81;print1(a=1,",",b=1,",");for(n=3,m,print1(c=if(a+b>n,abs(a-b),a+b),",");a=b;b=c)
%o A096062 (PARI) Vec(x*(2*x^13 -2*x^12 +x^11 +5*x^10 -x^9 -x^8 +x^7 +x^6 -x^5 +3*x^4 +x^3 +x^2 +x +1) / ((x -1)^2*(x +1)*(x^2 -x +1)*(x^2 +x +1)^2*(x^4 -x^2 +1)) + O(x^100)) \\ _Colin Barker_, Mar 12 2015
%K A096062 nonn,easy
%O A096062 1,3
%A A096062 _Amarnath Murthy_, Jun 18 2004
%E A096062 Edited, corrected and extended by _Klaus Brockhaus_, Jun 19 2004