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 A171442 Expansion of (1+x)^7/(1-x). 7
 1, 8, 29, 64, 99, 120, 127, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128, 128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n)=2^7=128 for n>=7. We observe that this sequence is the transform of A171441 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,...). REFERENCES (Revue bimestrielle), Richard Choulet, Une nouvelle formule de combinatoire ?, Mathématique et Pédagogie, 157 (2006), 53-60. LINKS Index entries for linear recurrences with constant coefficients, signature (1). FORMULA With m=8, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k). EXAMPLE a(5) = C(8,5-0)+C(8,5-2)+C(8,5-4) = 56+56+8 = 120. MAPLE m:=8: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); MATHEMATICA CoefficientList[Series[(1+x)^7/(1-x), {x, 0, 60}], x] (* Harvey P. Dale, Apr 30 2012 *) CROSSREFS Cf. A040000, A113311, A115291, A171418, A171440, A171441, A171443. Sequence in context: A299802 A299678 A300310 * A341402 A247541 A320695 Adjacent sequences:  A171439 A171440 A171441 * A171443 A171444 A171445 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 13 12:16 EDT 2021. Contains 343839 sequences. (Running on oeis4.)