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A003661 Number of bipartite Steinhaus graphs on n nodes.
(Formerly M0996)
1
1, 2, 4, 6, 9, 10, 13, 15, 19, 19, 21, 23, 27, 28, 31, 34, 39, 38, 39, 40, 43, 44, 47, 50, 55, 55, 57, 59, 63, 65, 69, 73, 79, 77, 77, 77, 79, 79, 81, 83, 87, 87, 89, 91, 95, 97, 101, 105, 111, 110, 111, 112, 115, 116, 119, 122, 127, 128, 131, 134, 139, 142, 147, 152, 159 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

W. M. Dymacek, M. Koerlin and T. Whaley, A survey of Steinhaus graphs, Proc. 8th Quadrennial International Conf. on Graph Theory, Combinatorics, Algorithms and Application, Kalamazoo, Mich. 1996, pages 313-323, Vol. I.

W. M. Dymacek and T. Whaley, Generating strings for bipartite Steinhaus graphs, Discrete Math. 141 (1995), pages 97-107.

Hsien-Kuei Hwang, S Janson, TH 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; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585

N. 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=1..65.

FORMULA

a(n) <= (5n-7)/2 (n > 2) with equality for n=2^k + 1.

a(2k+1)=2a(k+1)+1; a(2k)=a(k)+a(k+1) for k >=2.

MAPLE

a := proc(n) if n=1 then 1 elif n=2 then 2 elif n=3 then 4 elif n mod 2 = 1 then 2*a((n+1)/2) + 1 else a(n/2)+a(n/2+1) fi end: seq(a(n), n=1..80);

CROSSREFS

Sequence in context: A050110 A184416 A187225 * A065387 A219787 A065388

Adjacent sequences:  A003658 A003659 A003660 * A003662 A003663 A003664

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from Emeric Deutsch, Feb 26 2004

STATUS

approved

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Last modified November 16 06:50 EST 2018. Contains 317258 sequences. (Running on oeis4.)