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A192484 Shifts left under XOR-convolution: a(n) = Sum_{k=0..n-1} a(k) XOR a(n-k-1) for n>1 with a(0)=1, a(1)=2. 4
1, 2, 6, 14, 38, 102, 294, 854, 2566, 7622, 22790, 68166, 204678, 613318, 1839750, 5518310, 16553798, 49656774, 148968774, 446888518, 1340652486, 4021929542, 12065804486, 36197270598, 108591619654, 325774522822, 977323956550 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Limit a(n+1)/a(n) = 3.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

EXAMPLE

Given a(0)=1, a(1)=2, illustrate XOR convolution for the initial terms.

a(2) = 1 XOR 2 + 2 XOR 1 = 3 + 3 = 6;

a(3) = 1 XOR 6 + 2 XOR 2 + 6 XOR 1 = 7 + 0 + 7 = 14;

a(4) = 1 XOR 14 + 2 XOR 6 + 6 XOR 2 + 14 XOR 1 = 15 + 4 + 4 + 15 = 38; ...

PROG

(PARI) {a(n)=if(n<2, n+1, sum(k=0, n-1, bitxor(a(k), a(n-k-1))))}

(Haskell)

import Data.Bits (xor)

a192484 n = a192484_list !! n

a192484_list = 1 : 2 : f [2, 1] where

   f xs = y : f (y : xs) where

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

-- Reinhard Zumkeller, Jul 15 2012

CROSSREFS

Cf. variant: A007462.

Cf. A199770.

Sequence in context: A000634 A006654 A127546 * A217861 A188492 A263732

Adjacent sequences:  A192481 A192482 A192483 * A192485 A192486 A192487

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 02 2011

STATUS

approved

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Last modified December 1 12:40 EST 2020. Contains 338833 sequences. (Running on oeis4.)