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A101399
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a(0) = 1, a(1) = 2, a(2) = 5; for n >= 3, a(n) = a(n-1) + 2*a(n-2) + a(n-3).
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7
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1, 2, 5, 10, 22, 47, 101, 217, 466, 1001, 2150, 4618, 9919, 21305, 45761, 98290, 211117, 453458, 973982, 2092015, 4493437, 9651449, 20730338, 44526673, 95638798, 205422482, 441226751, 947710513, 2035586497, 4372234274
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OFFSET
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0,2
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COMMENTS
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Lengths of successive words (starting with a) under the substitution: {a -> ab, b -> aac, c -> a}.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Dun Qiu, Classical pattern distributions in Sn(132) and Sn(123), arXiv:1810.10099 [math.CO], 2018. See p. 11.
Index entries for linear recurrences with constant coefficients, signature (1, 2, 1).
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FORMULA
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G.f.: (1+x+x^2)/(1-x-2*x^2-x^3). - G. C. Greubel, Apr 03 2018
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MATHEMATICA
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a[0] = 1; a[1] = 2; a[2] = 5; a[n_] := a[n] = a[n - 1] + 2a[n - 2] + a[n - 3]; Table[ a[n], {n, 0, 30}] (* Robert G. Wilson v, Jan 15 2005 *)
LinearRecurrence[{1, 2, 1}, {1, 2, 5}, 30] (* Harvey P. Dale, Aug 29 2012 *)
CoefficientList[Series[(1+x+x^2)/(1-x-2*x^2-x^3), {x, 0, 50}], x] (* G. C. Greubel, Apr 03 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec((1+x+x^2)/(1-x-2*x^2-x^3)) \\ G. C. Greubel, Apr 03 2018
(Magma) I:=[1, 2, 5]; [n le 3 select I[n] else Self(n-1) + 2*Self(n-2) + Self(n-3): n in [1..30]]; /* or */ m:=25; R<x>:=PowerSeriesRing( Integers(), m); Coefficients(R!((1+x+x^2)/(1-x-2*x^2-x^3))); // G. C. Greubel, Apr 03 2018
(GAP) a:=[1, 2, 5];; for n in [4..35] do a[n]:=a[n-1]+2*a[n-2]+a[n-3]; od; a; # Muniru A Asiru, Apr 03 2018
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CROSSREFS
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Pairwise sums of A078007. Bisection of A003410 and A058278.
Sequence in context: A018004 A124329 A144520 * A320650 A018109 A341020
Adjacent sequences: A101396 A101397 A101398 * A101400 A101401 A101402
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KEYWORD
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nonn,easy
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AUTHOR
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Jeroen F.J. Laros, Jan 15 2005
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EXTENSIONS
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More terms from Robert G. Wilson v and Lior Manor, Jan 15 2005
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STATUS
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approved
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