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

1,3

Links

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

Formula

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

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}]

Prog

(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

Crossrefs

Cf. A000108 (Catalan numbers).

Cf. A007462, A192484.

Sequence in context: A081154 A002900 A309087 * A204322 A196593 A248735

Adjacent sequences: A199767 A199768 A199769 * A199771 A199772 A199773

Keyword

nonn,easy

Author

Jacob A. Siehler, Nov 10 2011

Status

approved