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 A007464 Shifts left under GCD-convolution with itself. (Formerly M0536) 9
 1, 1, 2, 3, 4, 6, 6, 11, 10, 18, 16, 20, 24, 26, 20, 45, 40, 38, 34, 62, 46, 54, 50, 84, 50, 102, 78, 104, 98, 90, 70, 189, 82, 130, 84, 120, 112, 130, 120, 232, 152, 234, 132, 130, 208, 282, 140, 462, 180, 210, 220, 418, 284, 334, 260, 520, 156, 334, 556 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002. M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] MAPLE a:= proc(n) option remember;       `if`(n=0, 1, add(igcd(a(i), a(n-1-i)), i=0..n-1))     end: seq(a(n), n=0..80);  # Alois P. Heinz, Jun 22 2012 MATHEMATICA a[0]=1; a[1]=1; a[n_] := a[n] = Sum[GCD[a[k], a[n-k-1]], {k, 0, n-1}]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Sep 07 2012, after Alois P. Heinz *) PROG (PARI) N=66; v=vector(N);  v[1]=1; for(n=2, N, v[n]=sum(k=1, n-1, gcd(v[k], v[n-k])) ); v  \\ Joerg Arndt, Jun 30 2013 (Haskell) a007464 n = a007464_list !! n a007464_list = 1 : 1 : f [1, 1] where    f xs = y : f (y:xs) where y = sum \$ zipWith gcd xs \$ reverse xs -- Reinhard Zumkeller, Jan 21 2014 (Python) from fractions import gcd A007464_list = [1, 1] for n in range(1, 10**3):     A007464_list.append(sum(gcd(A007464_list[i], A007464_list[n-i]) for i in range(n+1))) # Chai Wah Wu, Dec 26 2014 CROSSREFS Cf. A178063 (partial sums). Sequence in context: A332295 A332576 A028335 * A210733 A265564 A064764 Adjacent sequences:  A007461 A007462 A007463 * A007465 A007466 A007467 KEYWORD nonn,nice,eigen AUTHOR STATUS approved

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)