OFFSET
2,2
REFERENCES
Fishburn, Peter C.; Roberts, Fred S., Uniqueness in finite measurement. Applications of combinatorics and graph theory to the biological and social sciences, 103--137, IMA Vol. Math. Appl., 17, Springer, New York, 1989. MR1009374 (90e:92099)
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..70
Peter C. Fishburn and Fred S. Roberts, Uniqueness in finite measurement, in Applications of combinatorics and graph theory to the biological and social sciences, 103--137, IMA Vol. Math. Appl., 17, Springer, New York, 1989. MR1009374 (90e:92099). [Annotated scan of five pages only]
Peter C. Fishburn and Fred S. Roberts, Elementary sequences, sub-Fibonacci sequences, Discrete Appl. Math. 44 (1993), no. 1-3, 261-281.
FORMULA
See the Maple program; f[k](x, y) is the number of sequences s[1], s[2], ..., s[k+2] such that s[1]=x, s[2]=y, s[j-1] <=s[j] <= s[j-2]+s[j-1]. - Emeric Deutsch and Don Reble, Feb 07 2005
EXAMPLE
G.f. = x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 31*x^6 + 127*x^7 + 711*x^8 + 5621*x^9 + ...
a(4)=4 because we have (1,1,1,1), (1,1,1,2), (1,1,2,2), (1,1,2,3).
MAPLE
f[0]:=1:for k from 0 to 19 do f[k+1]:=expand(sum(subs({x=y, y=z}, f[k]), z=y..x+y)) od: seq(subs({x=1, y=1}, f[k]), k=0..19);
PROG
(PARI) {a(n) = if(n<2, return(0)); my(c, e); forvec(s=vector(n, i, [1, fibonacci(i)]), e=0; for(k=3, n, if( s[k-1]>s[k] || s[k]>s[k-2]+s[k-1], e=1; break)); if(e, next); c++, 1); c}; /* Michael Somos, Dec 02 2016 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch and Don Reble, Feb 07 2005
STATUS
approved