A261890 Second differences of A055615, first differences of A261869.

2, 4, -8, 16, -24, 20, -7, 10, -31, 32, -24, 40, -26, -16, -2, 34, -36, 38, 2, -20, -46, 68, -23, 26, -52, 26, -29, 28, 0, 32, 2, -32, 0, -36, -2, 112, -74, -40, -2, 40, 0, 44, -43, 46, -139, 140, -47, 0, 51, -102, -2, 106, 2, -110, 112, -56, -118, 176, -120

Offset: 1

Author

Reinhard Zumkeller, Sep 05 2015

Keywords

• sign

Comments

a(n) = (n+2)*mu(n+2) - 2*(n+1)*mu(n+1) + n*mu(n), where mu = A008683 (Moebius function);

a(A114180(n)) = 0;

abs(a(n)) <= 4*(n+1).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008683, A055615, A261869, A114180.

Programs

Haskell

import Data.List (genericIndex)
a261890 n = genericIndex a261890_list (n - 1)
a261890_list = zipWith (-) (tail a261869_list) a261869_list

Mathematica

Differences[Table[n MoebiusMu[n],{n,80}],2] (* Harvey P. Dale, Mar 12 2023 *)

Formula

a(n) = A055615(n+2) - 2*A055615(n+1) + A055615(n).