A007463 Shifts left under lcm-convolution with itself.

1, 1, 2, 5, 14, 40, 128, 369, 1214, 3516, 12776, 40534, 137404, 463232, 1602348, 5216253, 17753898, 58597316, 212150928, 710453534, 2366853608, 8584498376, 30026959300, 100396304016, 333997297900, 1157269900344, 3852364562536, 13917848281928, 45618032373712

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• eigen

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..550
• 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 arXiv version]
• 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]

Programs

Maple

a:= proc(n) option remember;
      `if`(n=0, 1, add(ilcm(a(i), a(n-1-i)), i=0..n-1))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jun 22 2012

Mathematica

a[0]=1; a[1]=1; a[n_] := a[n] = Sum[LCM[a[k], a[n-k-1]], {k, 0, n-1}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Sep 07 2012, after Alois P. Heinz *)

PARI

N=66; v=vector(N);  v[1]=1; for(n=2,N, v[n]=sum(k=1,n-1, lcm(v[k],v[n-k])) ); v  \\ Joerg Arndt, Jun 30 2013