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

%I A171440 #37 Mar 19 2023 08:21:13
%S A171440 1,6,16,26,31,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,
%T A171440 32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,
%U A171440 32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32,32
%N A171440 Expansion of (1+x)^5/(1-x).
%C A171440 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,...).
%C A171440 Also continued fraction expansion of  (229657824-sqrt(257))/197139199. - _Bruno Berselli_, Sep 23 2011
%H A171440 Vincenzo Librandi, <a href="/A171440/b171440.txt">Table of n, a(n) for n = 0..100</a>
%H A171440 Richard Choulet, <a href="https://mp.sbpm.be/MP157.PDF">Une nouvelle formule de combinatoire?</a>, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
%H A171440 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A171440 With m=6, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
%e A171440 a(4) = C(6,4-0)+C(6,4-2)+C(6,4-4) = 15+15+1 = 31.
%t A171440 PadRight[{1,6,16,26,31},100,32] (* _Harvey P. Dale_, Oct 01 2013 *)
%Y A171440 Cf. A040000, A113311, A115291, A171418, A171441, A171442, A171443.
%K A171440 nonn,easy
%O A171440 0,2
%A A171440 _Richard Choulet_, Dec 09 2009
%E A171440 Definition rewritten by _Bruno Berselli_, Sep 23 2011