A192484 -id:A192484 - cp's OEIS frontend

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

N. J. A. Sloane

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

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]

Cf. A192484, A199770.

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

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

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 *)

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

A199770 Self-convolution with "addition" played by bitwise XOR.

Original entry on oeis.org

1, 0, 2, 6, 18, 50, 146, 426, 1282, 3810, 11394, 34082, 102338, 306658, 919874, 2759154, 8276898, 24828386, 74484386, 223444258, 670326242, 2010964770, 6032902242, 18098635298, 54295809826, 162887261410, 488661978274, 1465985458850, 4397955924386

Offset: 1

Jacob A. Siehler, Nov 10 2011

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A000108 (Catalan numbers).

Cf. A007462, A192484.

import Data.Bits (xor)
a199770 n = a199770_list !! (n-1)
a199770_list = 1 : f [1] where
   f xs = y : f (y : xs) where
     y = sum $ zipWith xor xs $ reverse xs :: Integer
-- Reinhard Zumkeller, Jul 15 2012

a:= proc(n) option remember; `if`(n=0, 1, add(
      Bits[Xor](a(i), a(n-1-i)), i=0..n-1))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Jun 16 2018

a[1] = 1; a[n_] := a[n] = Sum[BitXor[a[i], a[n - i]], {i, 1, n - 1}]; Table[a[n], {n, 30}]

a(1)=1, a(n) = sum ( a(i) XOR a(n-i), i = 1 .. n-1).

A318619 a(0) = 0, a(1) = 1; for n > 1, a(n) = Sum_{k=0..n-2} a(k) XOR a(n-k-2).

Original entry on oeis.org

0, 1, 0, 2, 0, 6, 6, 18, 26, 66, 110, 242, 450, 922, 1826, 3674, 7290, 14586, 29178, 58410, 116538, 233258, 466114, 932426, 1864586, 3729274, 7457386, 14915578, 29828762, 59659322, 119313866, 238631866, 477253498, 954516442, 1909012410, 3818036378, 7636034202

Offset: 0

Ilya Gutkovskiy, Aug 30 2018

nonn

N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, XOR

Cf. A007462, A192484.

a:= proc(n) option remember; `if`(n<2, n,
      add(Bits[Xor](a(k), a(n-k-2)), k=0..n-2))
    end:
seq(a(n), n=0..40); # Alois P. Heinz, Aug 30 2018

a[0] = 0; a[1] = 1; a[n_] := a[n] = Sum[BitXor[a[k], a[n - k - 2]], {k, 0, n - 2}]; Table[a[n], {n, 0, 36}]

a(n) ~ c * 2^n, where c = 0.111118791917413048987034558666...

cp's OEIS Frontend

A007462 Shifts left under XOR-convolution with itself.

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A199770 Self-convolution with "addition" played by bitwise XOR.

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Author

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Programs

Haskell

Maple

Mathematica

Formula

A318619 a(0) = 0, a(1) = 1; for n > 1, a(n) = Sum_{k=0..n-2} a(k) XOR a(n-k-2).

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Maple

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