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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?, Mathématique et Pédagogie, 157 (2006), p. 53-60. LINKS Index entries for linear recurrences with constant coefficients, signature (1). FORMULA With m=7, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k). 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 * A341401 A320694 A261465 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 May 8 09:57 EDT 2021. Contains 343666 sequences. (Running on oeis4.)