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A171440 Expansion of (1+x)^5/(1-x). 9
1, 6, 16, 26, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n)=2^5=32 for n>=5. We observe that this sequence is the transform of A171418 by T such that: T(u_0,u_1,u_2,u_3,u_4,u_5,...)=(u_0,u_0+u_1,u_1+u_2,u_2+u_3,u_3+u_4,...).
Also continued fraction expansion of (229657824-sqrt(257))/197139199. - _Bruno Berselli_, Sep 23 2011
LINKS
Richard Choulet, Une nouvelle formule de combinatoire?, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
FORMULA
With m=6, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
EXAMPLE
a(4) = C(6,4-0)+C(6,4-2)+C(6,4-4) = 15+15+1 = 31.
MATHEMATICA
PadRight[{1, 6, 16, 26, 31}, 100, 32] (* _Harvey P. Dale_, Oct 01 2013 *)
CROSSREFS
Sequence in context: A348229 A275641 A369886 * A031220 A011536 A283609
KEYWORD
nonn,easy
AUTHOR
_Richard Choulet_, Dec 09 2009
EXTENSIONS
Definition rewritten by _Bruno Berselli_, Sep 23 2011
STATUS
approved

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Last modified March 4 23:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)