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A141683
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An Padovan Invert transform of A000931 in an Vladeta Jovovic A001906 form: b(n)=b(n-2)+b(n-3); a(n)=Sum[b[k]*a(n - k), {k, 1, n}].
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0
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1, 1, 2, 4, 9, 19, 41, 88, 189, 406, 872, 1873, 4023, 8641, 18560, 39865, 85626, 183916, 395033, 848491, 1822473, 3914488, 8407925, 18059374, 38789712, 83316385, 178955183, 384377665, 825604416, 1773314929, 3808901426
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Essentially the same as A141015. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 2008]
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FORMULA
| b(n)=b(n-2)+b(n-3); a(n)=Sum[b[k]*a(n - k), {k, 1, n}].
a(n)=a(n-1)+2*a(n-2)+a(n-3), n>4. G.f.: x*(1-x^2-x^3)/(1-x-2*x^2-x^3). [Colin Barker, Feb 01 2012]
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MATHEMATICA
| Clear[b, a, n] (*A000931*) b[0] = 0; b[1] = 1; b[2] = 1; b[n_] := b[n] = b[n - 2] + b[n - 3]; Table[b[n], {n, 0, 30}]; a[0] = 1; a[n_] := a[n] = Sum[b[k]*a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 30}]
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CROSSREFS
| Cf. A000931, A001906.
Sequence in context: A184936 A142474 A141015 * A078039 A036622 A001384
Adjacent sequences: A141680 A141681 A141682 * A141684 A141685 A141686
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KEYWORD
| nonn,uned,changed
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 07 2008
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