Search: id:A007971
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%I A007971
%S A007971 0,1,2,2,4,8,18,42,102,254,646,1670,4376,11596,31022,83670,227268,
%T A007971 621144,1706934,4713558,13072764,36398568,101704038,285095118,
%U A007971 801526446,2259520830,6385455594,18086805002,51339636952,146015545604
%N A007971 INVERT transform of central trinomial coefficients (A002426).
%C A007971 For n>1, a(n) = 2(A005043(n-1)+A005043(n-2)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Jul 06 2003
%C A007971 Number of paths of a walk on the integers, allowing steps of size 0, 
               +1, and -1, which return to the starting point for the first time 
               at time n. [From David P. Sanders (dps(AT)fciencias.unam.mx), May 
               04 2009]
%F A007971 A002426(n) = Sum_{i=1..n} a(i)*A002426(n-i), n>0.
%F A007971 G.f.: 1-sqrt(1-2*x-3*x^2).
%F A007971 a(0)=0, a(1)=1, a(2)=2, then a(n)= (1/2) *(a(1)*a(n-1)+a(2)*a(n-2)+....+a(n-1)*a(1)) 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 24 2003
%Y A007971 Cf. A002426. A001006(n)=A007971(n+2)/2.
%Y A007971 Cf. A025227.
%Y A007971 Sequence in context: A108774 A063402 A139800 this_sequence A126068 A167022 
               A005702
%Y A007971 Adjacent sequences: A007968 A007969 A007970 this_sequence A007972 A007973 
               A007974
%K A007971 nonn
%O A007971 0,3
%A A007971 David Dumas (dumas(AT)TCNJ.EDU)

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