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A005269
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a(n) = number of length-n sequences s with s[1]=1, s[2]=1, s[k-1] <=s[k] <= s[k-2]+s[k-1] (s is called a sub-Fibonacci sequence of length n).
(Formerly M1234)
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2
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1, 2, 4, 10, 31, 127, 711, 5621, 64049, 1067599, 26287664, 963023487, 52766766100, 4342736509018, 538755914902622, 101067429677072459, 28751803102222498512, 12436935036300286507123, 8200693250120852291693833
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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REFERENCES
| Fishburn, Peter C.; Roberts, Fred S.; Elementary sequences, sub-Fibonacci sequences. Discrete Appl. Math. 44 (1993), no. 1-3, 261-281.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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 (deutsch(AT)duke.poly.edu) and Don Reble (djr(AT)nk.ca), Feb 07 2005
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EXAMPLE
| a(4)=4 because we have (1,1,1,1), (1,1,1,2), (1,1,2,2), (1,1,2,3).
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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);
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CROSSREFS
| Sequence in context: A007177 A138415 A005268 * A070900 A151400 A071954
Adjacent sequences: A005266 A005267 A005268 * A005270 A005271 A005272
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Don Reble (djr(AT)nk.ca), Feb 07 2005
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