A322407 Compound sequence a(n) = A319198(A278039(n)), for n >= 0.

0, 1, 3, 4, 4, 5, 7, 8, 9, 11, 12, 12, 13, 15, 16, 18, 19, 19, 20, 22, 23, 24, 26, 27, 27, 28, 30, 31, 31, 32, 34, 35, 36, 38, 39, 39, 40, 42, 43, 45, 46, 46, 47, 49, 50, 51, 53, 54, 54, 55, 57, 58, 59, 61, 62, 62, 63, 65, 66, 68, 69

Offset: 0

Author

Wolfdieter Lang, Jan 02 2019

Keywords

• nonn
• easy

Comments

Old name was: Compound tribonacci sequence a(n) = A319198(A278039(n)), for n >= 0.

a(n) gives the sum of the entries of the tribonacci word sequence t = A080843 not exceeding t(B(n)), with B(n) = A278039(n).

Examples

			n = 3: B(3) = 6, t = {0, 1, 0, 2, 0, 1, 0, ...} which sums to 4 = a(3) = -12 + 3*6 - 2, because A(3) = 12.
		

Crossrefs

Cf. A080843, A278040, A278039, A319198, A321333, A322408.

Formula

a(n) = z(B(n)) = Sum_{j=0..B(n)} t(j), n >= 0, with z = A319198, B = A278039 and t = A080843.

a(n) = -A(n) + 3*B(n) - (n - 1), where A(n) = A278040(n). For a proof see the W. Lang link in A080843, Proposition 8, eq. (46).

a(n) = Sum_{k=1..n-1} d(k), where d is the tribonacci sequence on the alphabet {1,2,0}. - Michel Dekking, Oct 08 2019

Extensions

Name changed by Michel Dekking, Oct 07 2019