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

0,4

Comments

Essentially diagonal sums of Pascal's triangle modulo 3.

Links

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

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A002487, A051638.

Sequence in context: A131340 A337121 A175470 * A317638 A002307 A287707

Adjacent sequences: A098531 A098532 A098533 * A098535 A098536 A098537

Keyword

easy,nonn

Author

Paul Barry, Sep 13 2004

Status

approved