A005204 Coding a recurrence.

0, 0, 0, 1, 2, 4, 9, 38, 308, 4937, 316006, 161795380, 1325427757897, 694905868332618342, 186537373642942364470529332, 410200022670422956346283949740775609161, 472928427326946774459561651845917849178636866326243365478

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Consider a rabbits generation tree, and code each level with 0 for a single segment, and 1 for a branched segment. The current sequence written in binary: 0, 0, 0, 1, 10, 100, is obtained with this scheme applied on sequence A000930, and follows recurrence formula a(n+3) = 2^A000930(n-1)*a(n+2) + a(n), when n >= 3. Note that the Fib. Quart. article gives incorrect value of 158022 for a(10). - Michel Marcus, Jul 29 2013

References

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

Links

• Eric M. Schmidt, Table of n, a(n) for n = 0..20
• H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., Sequences associated with t-ary coding of Fibonacci's rabbits, Fib. Quart., 15 (1977), 311-318 (see Table 2 page 313).

Crossrefs

Cf. A005203 (same kind of encoding).

Programs

PARI

A000930(n) = sum(i=0, n\3, binomial(n-2*i, i))
a(n) =  if (n==0, 0, if (n==1, 0, if (n==2, 0, if (n==3, 1, 2^A000930(n-4)*a(n-1) + a(n-3))))) \\ Michel Marcus, Jul 29 2013

Extensions

a(10) corrected and sequence extended by Michel Marcus, Jul 29 2013

More terms from Eric M. Schmidt, Jul 11 2015