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A007464 Shifts left under GCD-convolution with itself.

%I A007464 M0536 #45 Jun 28 2025 09:28:24
%S A007464 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,
%T A007464 102,78,104,98,90,70,189,82,130,84,120,112,130,120,232,152,234,132,
%U A007464 130,208,282,140,462,180,210,220,418,284,334,260,520,156,334,556
%N A007464 Shifts left under GCD-convolution with itself.
%D A007464 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007464 Alois P. Heinz, <a href="/A007464/b007464.txt">Table of n, a(n) for n = 0..10000</a>
%H A007464 M. Bernstein and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002.
%H A007464 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%p A007464 a:= proc(n) option remember;
%p A007464       `if`(n=0, 1, add(igcd(a(i), a(n-1-i)), i=0..n-1))
%p A007464     end:
%p A007464 seq(a(n), n=0..80);  # _Alois P. Heinz_, Jun 22 2012
%t A007464 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_ *)
%o A007464 (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
%o A007464 (Haskell)
%o A007464 a007464 n = a007464_list !! n
%o A007464 a007464_list = 1 : 1 : f [1,1] where
%o A007464    f xs = y : f (y:xs) where y = sum $ zipWith gcd xs $ reverse xs
%o A007464 -- _Reinhard Zumkeller_, Jan 21 2014
%o A007464 (Python)
%o A007464 from math import gcd
%o A007464 A007464_list = [1, 1]
%o A007464 for n in range(1,10**3):
%o A007464     A007464_list.append(sum(gcd(A007464_list[i],A007464_list[n-i]) for i in range(n+1)))
%o A007464 # _Chai Wah Wu_, Dec 26 2014
%Y A007464 Cf. A178063 (partial sums).
%K A007464 nonn,nice,eigen
%O A007464 0,3
%A A007464 _N. J. A. Sloane_