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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}]. 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

Table of n, a(n) for n=1..101.

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: A080736 A326127 A276151 * A240491 A113750 A282627

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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Last modified September 17 19:12 EDT 2019. Contains 327137 sequences. (Running on oeis4.)