A229144 - OEIS

%I #15 Aug 18 2024 15:07:19

%S 0,1,2,4,4,6,8,9,9,10,11,13,13,15,17,18,18,19,20,22,22,24,26,27,27,28,

%T 29,31,31,33,35,36,36,37,38,40,40,42,44,45,45,46,47,49,49,51,53,54,54,

%U 55,56,58,58,60,62,63,63,64,65,67,67,69,71,72,72,73,74,76,76,78,80,81,81,82,83,85,85,87,89

%N Partial sums of (Fibonacci numbers mod 3).

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 1, -1).

%F G.f.: (x+x^2+2*x^3+2*x^5+2*x^6+x^7)/((1-x^8)*(1-x)). [_Joerg Arndt_, Sep 15 2013]

%e The first F(n) are 0, 1, 1, 2, 3, 5, 8,... mod 3 this becomes 0, 1, 1, 2, 0, 2, 2,... so a(n) starts 0, 1, 2, 4 ,4, 6, 8, ...

%t Accumulate[Mod[Fibonacci[Range[0,80]],3]] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,1,-1},{0,1,2,4,4,6,8,9,9},80] (* _Harvey P. Dale_, Aug 18 2024 *)

%o (JavaScript)

%o N=50;

%o f=new Array();

%o f[0]=0; f[1]=1;

%o for (i=2;i<N;i++)  f[i]=f[i-1]+f[i-2];

%o fs=0;

%o for (i=0;i<N;i++) { fs+=f[i]%3; document.write(fs+', '); }

%o (PARI) concat([0], Vec( (x+x^2+2*x^3+2*x^5+2*x^6+x^7)/((1-x^8)*(1-x)) + O(x^166) ) ) \\ _Joerg Arndt_, Sep 15 2013

%Y Cf. A000045, A082115.

%K nonn

%O 0,3

%A _Jon Perry_, Sep 15 2013