A005595 States of a dynamic storage system.

1, 2, 4, 7, 13, 23, 46, 88, 186, 395, 880, 1989, 4644, 10934, 26210, 63319, 154377, 378443, 933022, 2308956, 5735371, 14286907, 35683814, 89324137, 224057918, 563033978, 1417210456, 3572641303, 9018885121, 22796905055, 57692673962, 146167385344, 370710166434

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• C. G. Bower, Transforms
• M. D. McIlroy, The number of states of a dynamic storage system, Computer J., 25 (No. 3, 1982), 388-392.
• M. D. McIlroy, The number of states of a dynamic storage system, Computer J., 25 (No. 3, 1982), 388-392. (Annotated scanned copy)
• Index entries for sequences related to bracelets

Programs

PARI

seq(n)={Vec((2 - 2*x + x^3)/((1 - x)*(1 - x - x^2)) + sum(d=1, n, eulerphi(d)/d*log((1-x^d)/(1-3*x^d+x^(2*d)) + O(x*x^n))))/2} \\ Andrew Howroyd, Jun 20 2018

Formula

Also "DIK" (bracelet, indistinct, unlabeled) transform of 2, 1, 1, 1, ...

G.f.: ((2 - 2*x + x^3)/((1 - x)*(1 - x - x^2)) + Sum_{d>0} phi(d)*log((1-x^d)/(1-3*x^d+x^(2*d)))/d)/2. - Andrew Howroyd, Jun 20 2018

Extensions

Sequence extended by Christian G. Bower

Terms a(30) and beyond from Andrew Howroyd, Jun 20 2018