A007462 - OEIS

%I M1274 #30 Oct 07 2017 00:09:00

%S 0,1,2,4,14,38,118,338,1006,2990,8974,26862,80510,241390,723934,

%T 2171046,6512910,19536974,58608782,175821710,527470318,1582385678,

%U 4747139342,14241362318,42724100334,128172182990,384516408110,1153548740206,3460645850030,10381936700110

%N Shifts left under XOR-convolution with itself.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A007462/b007462.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%F a(n) ~ c * 3^n, where c = 0.151273188266276362886260408769663538575624024971525940842364624... . - _Vaclav Kotesovec_, Sep 10 2014

%p with(Bits):

%p a:= proc(n) option remember;

%p       `if`(n<2, n, add(Xor(a(i), a(n-1-i)), i=0..n-1))

%p     end:

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Jun 22 2012

%t 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_ *)

%o (Haskell)

%o import Data.Bits (xor)

%o a007462 n = a007462_list !! n

%o a007462_list = 0 : 1 : f [1,0] where

%o    f xs = y : f (y : xs) where

%o      y = sum $ zipWith xor xs $ reverse xs :: Integer

%o -- _Reinhard Zumkeller_, Jul 15 2012

%Y Cf. A192484, A199770.

%K nonn,nice,eigen

%O 0,3

%A _N. J. A. Sloane_