A007464 - OEIS

%I M0536 #41 Jun 10 2020 17:41:34

%S 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 102,78,104,98,90,70,189,82,130,84,120,112,130,120,232,152,234,132,

%U 130,208,282,140,462,180,210,220,418,284,334,260,520,156,334,556

%N Shifts left under GCD-convolution with itself.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A007464/b007464.txt">Table of n, a(n) for n = 0..10000</a>

%H 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 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 a:= proc(n) option remember;

%p       `if`(n=0, 1, add(igcd(a(i), a(n-1-i)), i=0..n-1))

%p     end:

%p seq(a(n), n=0..80);  # _Alois P. Heinz_, Jun 22 2012

%t 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 (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 (Haskell)

%o a007464 n = a007464_list !! n

%o a007464_list = 1 : 1 : f [1,1] where

%o    f xs = y : f (y:xs) where y = sum $ zipWith gcd xs $ reverse xs

%o -- _Reinhard Zumkeller_, Jan 21 2014

%o (Python)

%o from fractions import gcd

%o A007464_list = [1, 1]

%o for n in range(1,10**3):

%o     A007464_list.append(sum(gcd(A007464_list[i],A007464_list[n-i]) for i in range(n+1)))

%o # _Chai Wah Wu_, Dec 26 2014

%Y Cf. A178063 (partial sums).

%K nonn,nice,eigen

%O 0,3

%A _N. J. A. Sloane_