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A122576
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G.f.: (1-2*x+6*x^2-2*x^3+x^4)/((x-1)^3*(x+1)^4).
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2
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-1, 3, -12, 20, -45, 63, -112, 144, -225, 275, -396, 468, -637, 735, -960, 1088, -1377, 1539, -1900, 2100, -2541, 2783, -3312, 3600, -4225, 4563, -5292, 5684, -6525, 6975, -7936, 8448, -9537, 10115, -11340, 11988, -13357, 14079, -15600, 16400, -18081, 18963, -20812, 21780, -23805
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A model Fredholm minor 2 X 2 Fibonacci based matrix recursion determiant sequence (see Mathematica code). I had tried this type of matrix recursion before in A098023, but I think this method is better and more general.
Unsigned = row sums of triangle A143120 and SUM:{1..inf.} n*A026741(n); where A026741 = (1, 1, 3, 2, 5, 3, 7, 4, 9,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 26 2008
Unsigned, it appears the partial sums of positive integers of A129194. - Omar E. Pol, Aug 22 2011
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REFERENCES
| Roger G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, 1966; p. 254.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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MAPLE
| a:=n->(sum(-(numbperm(n, 2)), j=1..n/2)):seq(a(n)/2, n=2..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 12 2008
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MATHEMATICA
| gm = {{0, 1}, {1, 0}}; k = {{0, 1}, {1, 1}}; y[0] = {{0, 1}, {1, 1}}; y[n_] := y[n] = k*y[n - 1] + k*(y[n - 1][[1, 1]] + y[n - 1][[2, 2]])/n a = Table[Det[Sum[MatrixPower[gm, m].y[m], {m, 0, n}]], {n, 0, 25}]
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CROSSREFS
| Cf. A098023.
Cf. A143120, A026741.
Sequence in context: A199129 A063244 A063102 * A143268 A193558 A080767
Adjacent sequences: A122573 A122574 A122575 * A122577 A122578 A122579
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KEYWORD
| sign
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), May 20 2007. The simple generating function now used to define the sequence was found by an anonymous correspondent.
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