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).

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, 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, 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

Offset: 1

Author

Amarnath Murthy, Jun 18 2004

Keywords

• nonn
• easy

Comments

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

Examples

			a(8) + a(9) = 5 + 2 = 7 < 10, so a(10) = 7.
a(16) + a(17) = 15 + 17 = 32 > 18, so a(18) = abs(15 - 17) = 2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,-1,-1,1,1,-1,-1,1,1,0,-1).

Programs

Mathematica

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 *)

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)

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

Formula

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

Extensions

Edited, corrected and extended by Klaus Brockhaus, Jun 19 2004