A321333 Compound sequence with a(n) = A319198(A278040(n)), for n >= 0.

1, 4, 5, 8, 9, 12, 13, 16, 19, 20, 23, 24, 27, 28, 31, 32, 35, 36, 39, 40, 43, 46, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 69, 70, 73, 74, 77, 78, 81, 82, 85, 86, 89, 90, 93, 96, 97, 100, 101, 104, 105, 108, 111, 112, 115, 116, 119, 120, 123, 124, 127

Offset: 0

Author

Wolfdieter Lang, Dec 27 2018

Keywords

• nonn
• easy

Comments

Old name was: Compound tribonacci sequence a(n) = A319198(A278040(n)), for n >= 0.

a(n) gives the sum of the entries of the tribonacci word sequence t = A080843 not exceeding t(A(n)), with A(n) = A278040(n).

Examples

			n = 4, A(4) = 14, t = {0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, ...}, which sums to  9  = a(4) = 2*(14 - 7) - 5, because B(4) = 7.
		

Crossrefs

Cf. A080843, A278040, A278039, A319198, A322407, A322408.

Formula

a(n) = z(A(n)) = Sum_{j=0..A(n)} t(j), n >= 0, with z = A319198, A = A278040 and t = A080843.

a(n) = 2*(A(n) - B(n)) - (n + 1), where B(n) = A278039(n). For a proof see the W. Lang link in A080843, Proposition 8, eq. (45).

a(n)= 1 + Sum_{k=1..n-1} d(k), where d is the tribonacci sequence on the alphabet {3,1,1}. - Michel Dekking, Oct 08 2019

Extensions

Name changed by Michel Dekking, Oct 08 2019