A323365 Sum of Stern's Diatomic sequence, A002487 and its Dirichlet inverse, A317843.

2, 0, 0, 1, 0, 4, 0, 1, 4, 6, 0, 2, 0, 6, 12, 1, 0, 4, 0, 3, 12, 10, 0, 2, 9, 10, 8, 3, 0, -4, 0, 1, 20, 10, 18, 4, 0, 14, 20, 3, 0, 4, 0, 5, 4, 14, 0, 2, 9, 5, 20, 5, 0, 8, 30, 3, 28, 14, 0, 4, 0, 10, 20, 1, 30, -8, 0, 5, 28, 0, 0, 4, 0, 22, -2, 7, 30, 0, 0, 3, 16, 22, 0, 8, 30, 26, 28, 5, 0, 20, 30, 7, 20, 18, 42, 2, 0, 9, 4, 7, 0, 4, 0, 5, 0

Offset: 1

Author

Antti Karttunen, Jan 13 2019

Keywords

• sign
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to Stern's sequences

Crossrefs

Cf. A002487 (also a quadrisection of this sequence), A317843.

Cf. also A317837, A319687, A323885, A323887, A323894, A323896.

Programs

PARI

A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
A317843(n) = if(1==n,1,-sumdiv(n,d,if(dA002487(n/d)*A317843(d),0)));
A323365(n) = (A002487(n) + A317843(n));

Formula

a(n) = A002487(n) + A317843(n).

From Antti Karttunen, Dec 08 2021: (Start)

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A002487(d) * A317843(n/d).

a(4*n) = A002487(n).

(End)