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A113066
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Expansion of (1+x)^2/((x^2+x+1)*(x^2+3*x+1)).
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0
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1, -2, 4, -10, 27, -72, 189, -494, 1292, -3382, 8855, -23184, 60697, -158906, 416020, -1089154, 2851443, -7465176, 19544085, -51167078, 133957148, -350704366, 918155951, -2403763488, 6293134513, -16475640050, 43133785636, -112925716858, 295643364939, -774004377960
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform gives signed version of A093040. a(n) + a(n+1) = ((-1)^(n+1))A109961(n+1). a(n) + a(n+1) + a(n+2) = ((-1)^n)A001906(n+2) = ((-1)^n)F(2n+4)
The positive sequence has g.f. (1-x)^2/((1-x+x^2)(1-3x+x^2)) and a(n)=sum{k=0..n, C(n+k+1,n-k)*(1+(-1)^k)/2}. [From Paul Barry (pbarry(AT)wit.ie), Jul 06 2009]
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REFERENCES
| C. Dement, Floretion Integer Sequences (work in progress).
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FORMULA
| a(n) = A049347(n)/2 +(-1)^n*A001906(n+1)/2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2009]
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PROG
| Floretion Algebra Multiplication Program, FAMP Code: 2basei[C*F]; C = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki'; F = + .5'i + .5'ii' + .5'ij' + .5'ik'
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CROSSREFS
| Cf. A113067, A113068, A093040, A109961, A001906.
Sequence in context: A179981 A086991 A173758 * A002459 A104383 A205480
Adjacent sequences: A113063 A113064 A113065 * A113067 A113068 A113069
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KEYWORD
| easy,sign
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 13 2005
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