A007464 Shifts left under GCD-convolution with itself. (Formerly M0536)

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

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: A332576 A028335 A346117 * A210733 A265564 A064764

Adjacent sequences: A007461 A007462 A007463 * A007465 A007466 A007467

Keyword

nonn,nice,eigen

Author

N. J. A. Sloane

Status

approved