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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

REFERENCES

Richard Choulet, Une nouvelle formule de combinatoire?, Mathématique et Pédagogie, 157 (2006), p. 53-60.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (1).

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

Cf. A040000, A113311, A115291, A171418, A171441, A171442, A171443.

Sequence in context: A199988 A114222 A275641 * A031220 A011536 A283609

Adjacent sequences:  A171437 A171438 A171439 * A171441 A171442 A171443

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 April 11 18:00 EDT 2021. Contains 342888 sequences. (Running on oeis4.)