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 A005672 a(n) = Fibonacci(n+1) - 2^floor(n/2). (Formerly M3253) 24
 0, 0, 0, 1, 1, 4, 5, 13, 18, 39, 57, 112, 169, 313, 482, 859, 1341, 2328, 3669, 6253, 9922, 16687, 26609, 44320, 70929, 117297, 188226, 309619, 497845, 815656, 1313501, 2145541 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 REFERENCES R. K. Guy, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Table of n, a(n) for n=0..31. R. K. Guy, Letter to N. J. A. Sloane, 1987 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 FORMULA a(n) = Fibonacci(n-1) + 2*a(n-2), a(-1)=0, a(1)=0, a(2)=1. - Zerinvary Lajos, Mar 17 2008 MAPLE A005672:=z**3/(z**2+z-1)/(-1+2*z**2); # conjectured by Simon Plouffe in his 1992 dissertation with (combinat):a[ -1]:=0:a[1]:=0:a[2]:=1:for n from 2 to 50 do a[n]:=fibonacci(n-1)+2*a[n-2] od: seq(a[n-1], n=0..31); # Zerinvary Lajos, Mar 17 2008 CROSSREFS Gives diagonal sums of triangle A054143. Sequence in context: A234254 A258281 A094029 * A147001 A247325 A140683 Adjacent sequences: A005669 A005670 A005671 * A005673 A005674 A005675 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 26 09:24 EDT 2023. Contains 365654 sequences. (Running on oeis4.)