A006166 a(0)=0, a(1)=a(2)=1; for n >= 1, a(3n+2) = 2a(n+1) + a(n), a(3n+1) = a(n+1) + 2a(n), a(3n) = 3a(n). (Formerly M2270)

0, 1, 1, 3, 3, 3, 3, 5, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69

Offset

0,4

References

J. Arkin, D. C. Arney, L. S. Dewald and W. E. Ebel, Jr., Families of recursive sequences, J. Rec. Math., 22 (No. 22, 1990), 85-94.

vN. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..75.

Jean-Paul Allouche and Jeffrey Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29. [Preprint.]

Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, preprint, 2016.

Hsien-Kuei Hwang, Svante Janson and Tsung-Hsi Tsai, Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, Vol. 13, No. 4 (2017), Article #47.

Formula

From Peter Bala, Oct 08 2022: (Start)

a(n+2) - a(n) = 0 or 2.

a(3^k + j) = 3^k for k >= 0 and for 0 <= j <= 3^k.

a(2*3^k + j) = 3^k + 2*j for k >= 0 and for 0 <= j <= 3^k.

A081134(n) = n - a(n). (End)

Crossrefs

a(n) + n = A003605(n). Cf. A006165, A080678, A081134.

Sequence in context: A156724 A196186 A075753 * A339718 A349926 A268443

Adjacent sequences: A006163 A006164 A006165 * A006167 A006168 A006169

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 28 2003

Status

approved