A306216 Successive concatenation of the current sequence with the first differences of the sequence, a(1) = a(2) = 1.

1, 1, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 1, -1, 1, -1, 0, -1, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 2, -2, 2, -2, 0, -1, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1, 2, -2, 2, -2, 1, -1, 1, -1, 2, -2, 2, -2, 2, -2, 2, -2, 3, -4, 4, -4, 0, -1, 0, -1, 1, -1, 1, -1, 1, -1

Offset: 1

Author

Peter Kagey, Jan 29 2019

Keywords

• sign
• look

Comments

n | generation | first differences

--+------------------------+-------------------

1 | [1,1] | [0]

2 | [1,1,0] | [0,-1]

3 | [1,1,0,0,-1] | [0,-1,0,-1]

4 | [1,1,0,0,-1,0,-1,0,-1] | [0,-1,0,-1,1,-1,1,-1]

Links

• Peter Kagey, Table of n, a(n) for n = 1..8193 (first 14 generations)

Crossrefs

Cf. A107946, A306211.

Programs

Haskell

a306216_list = 1 : 1 : concat (Data.List.unfoldr nextGeneration [1,1]) where
  nextGeneration l = Just (diff l, l ++ diff l)
  diff xs =  zipWith subtract xs (tail xs)

Mathematica

Nest[Join[#, Differences@ #] &, {1, 1}, 7] (* Michael De Vlieger, Jan 29 2019 *)

Ruby

generations = 10
(1...generations).reduce([1,1]) do |s, _|
  s += s.each_cons(2).map { |a, b| b - a }
end