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%I M1199 #30 Jan 05 2025 19:51:33
%S 0,0,0,1,2,4,9,38,308,4937,316006,161795380,1325427757897,
%T 694905868332618342,186537373642942364470529332,
%U 410200022670422956346283949740775609161,472928427326946774459561651845917849178636866326243365478
%N Coding a recurrence.
%C 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
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Eric M. Schmidt, <a href="/A005204/b005204.txt">Table of n, a(n) for n = 0..20</a>
%H H. W. Gould, J. B. Kim and V. E. Hoggatt, Jr., <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/15-4/gould.pdf">Sequences associated with t-ary coding of Fibonacci's rabbits</a>, Fib. Quart., 15 (1977), 311-318 (see Table 2 page 313).
%o (PARI) A000930(n) = sum(i=0, n\3, binomial(n-2*i, i))
%o 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
%Y Cf. A005203 (same kind of encoding).
%K nonn
%O 0,5
%A _N. J. A. Sloane_
%E a(10) corrected and sequence extended by _Michel Marcus_, Jul 29 2013
%E More terms from _Eric M. Schmidt_, Jul 11 2015