[seqfan] Re: Simple seq with 3 in 4
Richard Mathar
mathar at strw.leidenuniv.nl
Sat Aug 21 19:48:44 CEST 2010
http://list.seqfan.eu/pipermail/seqfan/2010-August/005740.html says
ea> "To find 3 consecutive naturals in S,
ea> you have to take 4 consecutive terms
ea> of S -- no less":
ea> S= 1,3,0,2,4,1,3,5,2,4,6,3,5,7,4,6,8,5,7,9,6,8,10,7,9,11,8,10,...
Confirming Alex we see that this falls into the pattern
a(n)= +a(n-1) +a(n-3) -a(n-4)
= (n+3+5*A049347(n-1))/3 (assuming offset 0)
also known as the ocean of
<a href="Sindx_Rea.html#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
Generating function
(1+2*x+x^3-3*x^2)/(1+x+x^2)/(x-1)^2
These almost-no-growth sequences are bad for the economy.
RJM
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