A098534 Mod 3 analog of Stern's diatomic series.

0, 1, 1, 2, 3, 2, 2, 4, 3, 4, 7, 5, 6, 5, 5, 4, 6, 4, 4, 8, 6, 8, 8, 7, 6, 10, 7, 8, 15, 11, 14, 10, 12, 10, 13, 11, 12, 11, 11, 10, 12, 10, 10, 11, 9, 8, 14, 10, 12, 10, 10, 8, 12, 8, 8, 16, 12, 16, 13, 14, 12, 17, 14, 16, 18, 16, 16, 17, 15, 14, 17, 13, 12, 22, 16, 20, 18, 17, 14, 22

Offset: 0

Author

Paul Barry, Sep 13 2004

Keywords

• easy
• nonn

Comments

Essentially diagonal sums of Pascal's triangle modulo 3.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002487, A051638.

Programs

Magma

[0] cat [(&+[Binomial(n-k-1,k) mod 3: k in [0..Floor((n-1)/2)]]): n in [1..100]]; // G. C. Greubel, Jan 17 2018

Mathematica

Table[Sum[Mod[Binomial[n - k - 1, k], 3], {k, 0, Floor[(n - 1)/2]}], {n, 0, 100}] (* G. C. Greubel, Jan 17 2018 *)

PARI

for(n=0,100, print1(sum(k=0,floor((n-1)/2), lift(Mod(binomial(n-k-1,k),3))), ", ")) \\ G. C. Greubel, Jan 17 2018

Formula

a(n) = Sum_{k=0..floor((n-1)/2)} mod(binomial(n-k-1, k), 3).