A171440 Expansion of (1+x)^5/(1-x).

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

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

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

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

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: A348229 A275641 A369886 * 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