A319198 Partial sums of the infinite self-similar tribonacci word, written in the form A080843.

0, 1, 1, 3, 3, 4, 4, 4, 5, 5, 7, 7, 8, 8, 9, 9, 11, 11, 12, 12, 12, 13, 13, 15, 15, 16, 16, 18, 18, 19, 19, 19, 20, 20, 22, 22, 23, 23, 24, 24, 26, 26, 27, 27, 27, 28, 28, 30, 30, 31, 31, 31, 32, 32, 34, 34, 35, 35, 36, 36, 38, 38, 39, 39, 39, 40, 40, 42, 42, 43, 43

Offset: 0

Author

Wolfdieter Lang, Oct 10 2018

Keywords

• nonn
• easy

Comments

This sequence produces a formula for the A-numbers A278040, specifying the positions (or indices) of 1's in A080843, namely A(n) = 4*n+1 - a(n-1), with a(-1) = 0.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10600
• Wolfdieter Lang, The Tribonacci and ABC Representations of Numbers are Equivalent, arXiv preprint arXiv:1810.09787 [math.NT], 2018.

Crossrefs

Cf. A080843, A276797, A276798, A278039 (B-numbers), A278040 (A-numbers), A278041 (C-numbers).

Formula

a(n) = Sum_{j=0..n} A080843(n), n >= 0.

a(n) = z_A(n) + 2*z_C(n) = A276797(n+1) + 2*(A276798(n+1) - 1), where z_A(n) gives the number of A-numbers from A278040 not exceeding n, similarly for z_C(n) with the C-numbers from A278041. - Wolfdieter Lang, Dec 13 2018