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 A144412 Invert transform of odd non-prime 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}]. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Except for the first five elements, the inverse transform result seems to be zero. LINKS FORMULA b(n)=A067970(n)/2-2; a(n)=Sum[b(n + 1)*a(n - k), {k, 1, n}]. 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}] CROSSREFS Cf. A067970, A001906. Sequence in context: A030207 A061006 A080736 * A113750 A004565 A068449 Adjacent sequences:  A144409 A144410 A144411 * A144413 A144414 A144415 KEYWORD uned,sign AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 30 2008 STATUS approved

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