A058839 Expansion of (1-x^5)*Product_{r>=3} (1-x^r).

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

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

J. Fulman, Random matrix theory over finite fields, Bull. Amer. Math. Soc., 39 (No. 1, 2002), 51-85, see Theorem 1.

Mathematica

maxDeg=92;
a=SparseArray[{1->1}, maxDeg+1];
step[r_]:=Module[{b=ConstantArray[0, maxDeg+1]}, Do[b[[i+1]]+=a[[i+1]];
If[i+r<=maxDeg, b[[i+r+1]]-=a[[i+1]]], {i, 0, maxDeg}];
a=b];
Do[step[r], {r, 3, maxDeg}];
step[5];
a (* Vincenzo Librandi, Nov 26 2025 *)

Prog

(Magma) N := 100; R<x> := PowerSeriesRing(Integers(), N+1);
f := 1 - x^5; for r in [3..N] do f *:= 1 - x^r;
end for;  coeffs := [Coefficient(f, n) : n in [0..N]]; coeffs; // Vincenzo Librandi, Nov 26 2025

Crossrefs

Sequence in context: A321005 A055254 A035670 * A275946 A287824 A065364

Adjacent sequences: A058836 A058837 A058838 * A058840 A058841 A058842

Keyword

sign

Author

N. J. A. Sloane, Jan 01 2002

Status

approved