A144412 Invert transform of odd nonprime gaps adjusted to be from the set {2,1,0,-1}: b(n)=A067970(n)/2-2; a(n)=Sum[b(n + 1)*a(n - k), {k, 1, n}].

2, 2, 4, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 30 2008

Keywords

• uned
• sign

Comments

Except for the first five elements, the inverse transform result seems to be zero.

Crossrefs

Cf. A067970, A001906.

Programs

Mathematica

b = Flatten[Table[If[PrimeQ[2*n + 1], {}, 2*n + 1], {n, 0, 200}]]; c = Table[(b[[n + 1]] - b[[n]])/2 - 2, {n, 1, Length[b] - 1}]; a[0] = c[[1]]; a[n_] := a[n] = Sum[c[[n + 1]]*a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 100}]

Formula

b(n)=A067970(n)/2-2; a(n)=Sum[b(n + 1)*a(n - k), {k, 1, n}].