A007462 Shifts left under XOR-convolution with itself. (Formerly M1274)

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

0,3

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..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]

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A192484, A199770.

Sequence in context: A135960 A216630 A006611 * A053623 A035010 A349450

Adjacent sequences: A007459 A007460 A007461 * A007463 A007464 A007465

Keyword

nonn,nice,eigen

Author

N. J. A. Sloane

Status

approved