A007460 Shifts left under OR-convolution with itself.

1, 1, 2, 7, 20, 58, 174, 519, 1550, 4634, 13884, 41616, 124824, 374390, 1123288, 3369297, 10107324, 30320434, 90961626, 272878138, 818632094, 2455888346, 7367661682, 22102935920, 66308767426, 198926187730, 596778527246, 1790335274112, 5371006016314

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• eigen

References

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2097
• 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]

Programs

Haskell

import Data.Bits ((.|.))
a007460 n = a007460_list !! n
a007460_list = 1 : f [1,1] where
   f xs = x : f (x:xs) where
     x = sum $ zipWith (.|.) xs $ tail $ reverse xs :: Integer
-- Reinhard Zumkeller, Dec 29 2012

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      Bits[Or](a(i), a(n-1-i)), i=0..n-1))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Jun 22 2012, revised, Jun 16 2018

Mathematica

a[0]=1; a[1]=1; a[n_] := a[n] = Sum[BitOr[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 *)

Formula

a(n) ~ c * 3^n, where c = 0.23477965293553321256228091184896942343087043274059369777596946751928557... . - Vaclav Kotesovec, Sep 11 2014