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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
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: A332576 A028335 A346117 * A210733 A265564 A064764
KEYWORD
nonn,nice,eigen
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)