A007462 Shifts left under XOR-convolution with itself.

0, 1, 2, 4, 14, 38, 118, 338, 1006, 2990, 8974, 26862, 80510, 241390, 723934, 2171046, 6512910, 19536974, 58608782, 175821710, 527470318, 1582385678, 4747139342, 14241362318, 42724100334, 128172182990, 384516408110, 1153548740206, 3460645850030, 10381936700110

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..1000
• 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]

Crossrefs

Cf. A192484, A199770.

Programs

Haskell

import Data.Bits (xor)
a007462 n = a007462_list !! n
a007462_list = 0 : 1 : f [1,0] where
   f xs = y : f (y : xs) where
     y = sum $ zipWith xor xs $ reverse xs :: Integer
-- Reinhard Zumkeller, Jul 15 2012

Maple

with(Bits):
a:= proc(n) option remember;
      `if`(n<2, n, add(Xor(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]=0; a[1]=1; a[n_] := a[n] = Sum[BitXor[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 *)

Formula

a(n) ~ c * 3^n, where c = 0.151273188266276362886260408769663538575624024971525940842364624... . - Vaclav Kotesovec, Sep 10 2014