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

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to Stern's sequences

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, 1<d<n} A002487(d) * A317843(n/d).

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

(End)

Prog

(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(d<n, A002487(n/d)*A317843(d), 0)));
A323365(n) = (A002487(n) + A317843(n));

Crossrefs

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

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

Sequence in context: A323887 A349913 A346236 * A349135 A353336 A349126

Adjacent sequences: A323362 A323363 A323364 * A323366 A323367 A323368

Keyword

sign,look

Author

Antti Karttunen, Jan 13 2019

Status

approved