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A171441 Expansion of (1+x)^6/(1-x). 7
1, 7, 22, 42, 57, 63, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)=2^6=64 for n>=6. We observe that this sequence is the transform of A171440 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 1+(1233212607598+5*sqrt(41))/8688482797079. - Bruno Berselli, Sep 23 2011

REFERENCES

(Revue bimestrielle), Richard Choulet, Une nouvelle formule de combinatoire?, Mathematique et Pedagogie, 157 (2006), p. 53-60.

LINKS

Table of n, a(n) for n=0..69.

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

FORMULA

With m=7, a(n)=sum(C(m,n-2*k),k=0..floor(n/2)).

EXAMPLE

a(4)=C(7,4-0)+C(7,4-2)+C(7,4-4)=35+21+1=57.

MAPLE

m:=7:for n from 0 to 40 do a(n):=sum('binomial(m, n-2*k)', k=0..floor(n/2)): od : seq(a(n), n=0..40);

CROSSREFS

Cf. A040000, A113311, A115291, A171418, A171440, A171442, A171443.

Sequence in context: A031053 A063130 A275642 * A261465 A033954 A159227

Adjacent sequences:  A171438 A171439 A171440 * A171442 A171443 A171444

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 October 17 12:50 EDT 2018. Contains 316280 sequences. (Running on oeis4.)