A229144 Partial sums of (Fibonacci numbers mod 3).

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

Offset

0,3

Links

Table of n, a(n) for n=0..78.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 1, -1).

Formula

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]

Example

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, ...

Mathematica

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 *)

Prog

(JavaScript)
N=50;
f=new Array();
f[0]=0; f[1]=1;
for (i=2; i<N; i++)  f[i]=f[i-1]+f[i-2];
fs=0;
for (i=0; i<N; i++) { fs+=f[i]%3; document.write(fs+', '); }
(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

Crossrefs

Cf. A000045, A082115.

Sequence in context: A279667 A000061 A153176 * A263021 A112921 A339905

Adjacent sequences: A229141 A229142 A229143 * A229145 A229146 A229147

Keyword

nonn

Author

Jon Perry, Sep 15 2013

Status

approved