A005204 Coding a recurrence. (Formerly M1199)

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

Offset

0,5

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).

Prog

(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

Crossrefs

Cf. A005203 (same kind of encoding).

Sequence in context: A327057 A151891 A309340 * A204428 A162111 A241600

Adjacent sequences: A005201 A005202 A005203 * A005205 A005206 A005207

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

More terms from Eric M. Schmidt, Jul 11 2015

Status

approved