Code golf the best permutation Challenge

Given an integer n ≥ 4, output a permutation of the integers [0, n-1] with the property that no two consecutive integers are next to each other.  The value of a permutation pi is the sum of abs(pi[i] - i) for all indices i.

Examples


(1, 3, 0, 2) has value  6
(0, 2, 4, 1, 3)  has value 6
(0, 2, 4, 1, 3, 5) has value 6
(0, 2, 4, 1, 5, 3, 6) has value 8


Score of your answer

The score of your answer is the sum of the values of your permutations for n = 4 .. 14 plus the number of bytes your code takes.  The lower the score, the better.  Your code must give valid output for all those values of n.

You must be able to run your submission to completion on your machine.

In case of ties,  time of last edit that resulted in the relevant score will be the decider.

Isn't this the same question as this one?

Answers to the linked question will not be competitive for this question as they make no effort to optimize the value of a permutation. For example for n=10, the permutation [1, 3, 5, 7, 9, 0, 2, 4, 6, 8] given by most of the answers there gives a value of 30. You can do much better than that.

For the permutation part of the question, the optimal value overall is at most 120.  (Thank you to @Laikoni.)   Whereas Dennis's answer to the previous question scores 222. (Thank you to @user202729.)
CJam (60 bytes + 120 = 180 score)

{_5/4*8e!961=7_)er&lt;:A\,^e!{A\+}%{2ew::-:z1&amp;!},{_$.-:z1b}$0=}


Online test suite with integrated scoring

Extension up to n=24

Dissection

{
  _5/4*        e# Work out how much of the hard-coded prefix to use
  8e!961=7_)er e# Prefix [0 2 4 1 3 5 8 6]
               e# I identified this by brute forcing up to n=10 and looking for patterns
               e# I then used the identified prefix [0 2 4 1] to brute-force further
  &lt;:A          e# Take the desired prefix of the hard-coded array, and store a copy in A
  \,^e!        e# Generate all permutations of the values in [0 .. n-1] which aren't in A
  {A\+}%       e# Prepend A to each of them
  {            e# Filter...
    2ew::-     e#   Take each difference of two consecutive elements
    :z         e#   Find their absolute values
    1&amp;         e#   Test whether 1 is among those absolute values
    !          e#   Reject if it is
  },
  {            e# Sort by...
    _$.-       e#   Take pairwise differences of permutation with the identity
    :z         e#   Absolute values
    1b         e#   Add them (by interpreting in base 1)
  }$
  0=           e# Take the first
}