This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A282938 Recursive 2-parameter sequence allowing calculation of the Möbius function (not the same as A266378) 0
 1, -1, 1, -1, -1, 2, -1, 0, 1, -2, 1, 0, -1, 2, -1, -1, 3, -2, -1, 1, -1, 1, 1, 0, -2, 1, 1, -2, 1, 0, -1, 1, -1, 3, -1, 0, -1, -2, 1, 1, 1, -1, -1, 3, -2, -1, 1, -1, 2, -2, 1, 1, 0, 0, -1, -3, 2, 2, 0, 0, -2, 1, 0, 0, 1, -3, 2, 1, -1, 1, -2, 2, -2, 2, -2, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS The a(n,m) forms a table where each row has (n-1)*(n-2)/2+1 = A000124(n-2) elements. The index of the first row is n=1 and the index of the first column is m=0. The right diagonal a(n, A000217(n-2)) = A008683(n), Möbius numbers, for n>=1. LINKS FORMULA a(n,m) = a(n-1, m-n+1) - a(n-1, m) - a(n-1, nu(n-1))*U(n-1, m-1), where U(n,m) are coefficients of A231599, nu(n)=(n-1)*(n-2)/2, a(1,0)=1, a(n,m)=0 if m<0 and m>nu(n). Möbius(n) = a(n,nu(n)). EXAMPLE The first few rows starting from 1 follow: 1 -1 1, -1 -1, 2, -1, 0 1, -2, 1, 0, -1, 2, -1 -1, 3, -2, -1, 1, -1, 1, 1, 0, -2, 1, 1, -2, 1, 0, -1, 1, -1, 3, -1, 0, -1, -2, 1, 1, 1, -1, -1, 3, -2, -1, 1, -1, 2, -2, 1, 1, 0, 0, -1, -3, 2, 2, 0, 0, -2, 1, 0, 0} MATHEMATICA nu[n_]:=(n-1)*(n-2)/2 U[n_, m_] := U[n, m] = If[n > 1, U[n - 1, m - n + 1] - U[n - 1, m], 0] U[1, m_] := U[1, m] = If[m == 0, 1, 0] a[n_, m_] := a[n, m] = If[(m < 0) || (nu[n] < m), 0, a[n - 1, m - n + 1] - a[n - 1, m] - a[n - 1, nu[n - 1]]*U[n - 1, m - 1]] a[1, m_] := a[1, m] = If[m == 0, 1, 0] Table[Table[a[n, m], {m, 0, nu[n]}], {n, 1, 30}] Table[a[n, nu[n]], {n, 1, 50}] CROSSREFS Cf. A000124, A000217, A008683, A231599. Sequence in context: A284171 A286320 A194525 * A065368 A010751 A194523 Adjacent sequences:  A282935 A282936 A282937 * A282939 A282940 A282941 KEYWORD sign,tabf AUTHOR Gevorg Hmayakyan, Feb 25 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 20 07:27 EDT 2019. Contains 321345 sequences. (Running on oeis4.)