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

0,4

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.

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

Crossrefs

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

Sequence in context: A318241 A181742 A179843 * A243348 A136546 A278765

Adjacent sequences: A319195 A319196 A319197 * A319199 A319200 A319201

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 10 2018

Status

approved