A007461 Shifts left under AND-convolution with itself.

1, 1, 2, 1, 2, 4, 0, 5, 2, 4, 0, 10, 0, 12, 4, 13, 6, 12, 0, 18, 12, 20, 20, 36, 20, 36, 16, 44, 32, 60, 40, 73, 50, 56, 40, 58, 44, 52, 60, 84, 36, 112, 88, 108, 136, 132, 152, 178, 136, 232, 108, 260, 244, 256, 304, 288

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• eigen

Comments

a(A000225(n)) mod 2 = 1, a(A062289(n)) mod 2 = 0. [Reinhard Zumkeller, Apr 02 2012]

References

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• 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]

Crossrefs

Cf. A007460, A199770.

Programs

Haskell

import Data.Bits ((.&.))
a007461 n = a007461_list !! n
a007461_list = 1 : f [1,1] where
   f xs = x : f (x:xs) where
     x = sum $ zipWith (.&.) xs $ tail $ reverse xs :: Integer
-- Reinhard Zumkeller, Apr 02 2012

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      Bits[And](a(i), a(n-1-i)), i=0..n-1))
    end:
seq(a(n), n=0..80);  # Alois P. Heinz, Jun 16 2018

Mathematica

a[0]=1; a[1]=1; a[n_] := a[n] = Sum[BitAnd[a[k], a[n-k-1]], {k, 0, n-1}]; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Sep 07 2012 *)