A134749 First differences of permutational numbers : a(n)=A134640(n+1)-A134640(n).

1, 1, 3, 2, 4, 4, 4, 2, 6, 3, 9, 6, 9, 3, 18, 3, 21, 9, 6, 6, 15, 6, 6, 9, 21, 3, 18, 3, 9, 6, 9, 3, -34, 4, 16, 8, 16, 4, 52, 4, 36, 12, 12, 8, 48, 8, 12, 12, 36, 4, 52, 4, 16, 8, 16, 4, 108, 4, 16, 8, 16, 4, 152, 4, 56, 16, 8, 12, 24, 8, 32, 16, 32, 8, 28, 4, 36, 12, 12, 8, 84, 4, 36, 12, 12, 8, 28, 4, 56, 16, 8, 12, 144, 12, 8, 16, 56, 4, 28, 8, 12

Offset: 1

Author

Artur Jasinski, Nov 08 2007

Keywords

• sign

Comments

Negative numbers occur at n=!k = A007489(k) and {k=3,4,5,...}

Crossrefs

Cf. A007489, A134640, A134703, A134748, A134750.

Programs

Mathematica

a = {}; b = {}; Do[AppendTo[b, n]; w = Permutations[b]; Do[j = FromDigits[w[[m]], n + 1]; AppendTo[a, j], {m, 1, Length[w]}], {n, 0, 5}]; d = {}; Do[AppendTo[d, a[[n + 1]] - a[[n]]], {n, 1, Length[a] - 1}] ; d (*Artur Jasinski*)
Differences[Flatten[Table[FromDigits[#,n]&/@Permutations[Range[0,n-1]], {n,5}]]] (* Harvey P. Dale, Dec 09 2014 *)