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