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

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

Author

Jacob A. Siehler, Nov 10 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000108 (Catalan numbers).

Cf. A007462, A192484.

Programs

Haskell

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

Maple

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

Mathematica

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

Formula

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