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A144413
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Euler difference transform on the Padovan sequence A000931: b(n)=b(n-2)+b(n-3); a(n)=Sum[(-1)^m*Binomial[n, m]*b(n - m), {m, 0, n}].
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0
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0, 1, -1, 1, 0, -3, 10, -24, 49, -89, 145, -208, 245, -174, -176, 1121, -3185, 7137, -13920, 24301, -37926, 51256, -53615, 20407, 97265, -386224, 984549, -2083934, 3896480, -6537023, 9734175
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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REFERENCES
| Weisstein, Eric W. "Euler Transform." http://mathworld.wolfram.com/EulerTransform.html
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FORMULA
| b(n)=b(n-2)+b(n-3); a(n)=Sum[(-1)^m*Binomial[n, m]*b(n - m), {m, 0, n}].
a(n)= -3*a(n-1)-2*a(n-2)+a(n-3). G.f.: x(1+2x)/(1+3x+2x^2-x^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 21 2009]
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MATHEMATICA
| Clear[f, n, a]; a[0] = 0; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; f[n_] := Sum[(-1)^m*Binomial[n, m]*a[n - m], {m, 0, n}]; Table[f[n], {n, 0, 30}]
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CROSSREFS
| Cf. A000931, A000073, A073358.
Sequence in context: A105861 A041327 A029880 * A033811 A062446 A053208
Adjacent sequences: A144410 A144411 A144412 * A144414 A144415 A144416
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KEYWORD
| uned,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 30 2008
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