|
Search: id:A005270
|
|
|
| A005270 |
|
Number of sequences s of length n with s[1]=1, s[2]=1, s[j-1]<s[j]<=s[j-2]+s[j-1] for j>=3. (Formerly M1684)
|
|
+0 3
|
|
| 1, 1, 1, 2, 6, 27, 177, 1680, 23009, 455368, 13067353, 546378617, 33472296082, 3021920660821, 404374532614122, 80646410554881100, 24095492607316134304, 10837141045948365696938, 7369252748590790186483284, 11961418205662159081422825777494
(list; graph; listen)
|
|
|
OFFSET
|
2,4
|
|
|
COMMENT
|
The sequences of length n that are counted here are sub-Fibonacci sequences (A005269) with the property that its members, except for the initial two terms, strictly increase. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2007
|
|
REFERENCES
|
Fishburn, Peter C. and Roberts, Fred S.; Elementary sequences, sub-Fibonacci sequences. Discrete Appl. Math. 44 (1993), no. 1-3, 261-281.
|
|
FORMULA
|
a(n) equals the number of nodes in generation n-2 of the sub-Fibonacci tree (A125051) for n>=2. - Paul D. Hanna (pauldhanna(AT)juno.com), Nov 19 2006
See the Maple program; g[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] for j>=3. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2007
|
|
EXAMPLE
|
a(2)=6 because we have (1,1,2,3,4,5), (1,1,2,3,4,6), (1,1,2,3,4,7), (1,1,2,3,5,6), (1,1,2,3,5,7), and (1,1,2,3,5,8).
|
|
MAPLE
|
g[0]:=1:for k from 0 to 20 do g[k+1]:=expand(sum(subs({x=y, y=z}, g[k]), z=y+1..x+y)) od:seq(subs({x=1, y=1}, g[k]), k=0..20); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2007
|
|
CROSSREFS
|
Cf. A125051, A125052.
Cf. A005269.
Sequence in context: A058712 A070076 A130455 this_sequence A080839 A011834 A003513
Adjacent sequences: A005267 A005268 A005269 this_sequence A005271 A005272 A005273
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
a(12) from Paul D. Hanna (pauldhanna(AT)juno.com), Nov 19 2006
Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2007
|
|
|
Search completed in 0.002 seconds
|