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A319198
Partial sums of the infinite self-similar tribonacci word, written in the form A080843.
7
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
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 10 2018
STATUS
approved