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A095127
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a(n+3) = 2*a(n+2) + 3*a(n+1) - a(n); with a(1) = 1, a(2) = 4, a(3) = 10.
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3
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1, 4, 10, 31, 88, 259, 751, 2191, 6376, 18574, 54085, 157516, 458713, 1335889, 3890401, 11329756, 32994826, 96088519, 279831760, 814934251, 2373275263, 6911521519, 20127934576, 58617158446, 170706599101, 497136738964
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A sequence generated from the characteristic polynomial of A095125 and A095126.
a(n)/a(n-1) tends to a 2.9122291784..., a root of the polynomial x^3 - 2x^2 - 3x + 1; e.g. a(16)/a(15) = 11329756/3890401 = 2.912233...
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FORMULA
| M = a matrix having the same eigenvalues as the roots of the characteristic polynomial of A095125 and A095126: (x^3 - 2x^2 - 3x + 1). Then M^n * [1 1 1] = [p q r] where q = a(n) and p, r, are offset members of the same sequence.
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EXAMPLE
| a(7) = 751 = 2*a(6) + 3*a(5) - a(4) = 2*259 + 3*88 - 31.
a(4) = 31 = center term in M^4 * [1 1 1] = [10 31 88].
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MATHEMATICA
| a[1] = 1; a[2] = 4; a[3] = 10; a[n_] := a[n] = 2a[n - 1] + 3a[n - 2] - a[n - 3]; Table[ a[n], {n, 25}] (from Robert G. Wilson v Jun 01 2004)
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CROSSREFS
| Cf. A095125, A095126, A095128.
Sequence in context: A067142 A145453 A034730 * A006342 A135831 A015796
Adjacent sequences: A095124 A095125 A095126 * A095128 A095129 A095130
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 29 2004
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EXTENSIONS
| Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 01 2004
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