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A123005
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G.f. x^2/(1-2*x-49*x^2).
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0
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0, 1, 2, 53, 204, 3005, 16006, 179257, 1142808, 11069209, 78136010, 698663261, 5225991012, 44686481813, 345446523214, 2880530655265, 22687940948016, 186521884004017, 1484752874460818, 12109078065118469, 96971046978817020
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
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FORMULA
| a(n)= 2*a(n-1) +49*a(n-2).
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MATHEMATICA
| (* coefficient expansion*) l = 2; m = 7; p[x_] := -1 - l*x/m + x^2 q[x_] := ExpandAll[x^2*p[1/x]] Table[ SeriesCoefficient[ Series[x/q[x], {x, 0, 30}], n]*m^(n - 1), {n, 0, 30}]
(* Binet/ recursion *) f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == l*a[n - 1]/m + a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] ; a = Table[Rationalize[N[f[n]*m^(n - 1), 100], 0], {n, 0, 25}]
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CROSSREFS
| Cf. A002534.
Sequence in context: A041337 A139844 A130698 * A142477 A119112 A109791
Adjacent sequences: A123002 A123003 A123004 * A123006 A123007 A123008
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KEYWORD
| nonn,easy
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 23 2006
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EXTENSIONS
| Definition replaced by generating function - the Assoc. Eds. of the OEIS, Mar 27 2010
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