A127214 a(n) = 2^n*tribonacci(n) or (2^n)*A001644(n+1).
2, 12, 56, 176, 672, 2496, 9088, 33536, 123392, 453632, 1669120, 6139904, 22585344, 83083264, 305627136, 1124270080, 4135714816, 15213527040, 55964073984, 205867974656, 757300461568, 2785785413632, 10247716470784, 37696978288640, 138671105769472
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2,4,8).
Programs
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Magma
I:=[2,12,56]; [n le 3 select I[n] else 2*Self(n-1) + 4*Self(n-2) + 8*Self(n-3): n in [1..30]]; // G. C. Greubel, Dec 18 2017
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Mathematica
Table[Tr[MatrixPower[2*{{1, 1, 1}, {1, 0, 0}, {0, 1, 0}}, x]], {x, 1, 20}] LinearRecurrence[{2, 4, 8}, {2, 12, 56}, 50] (* G. C. Greubel, Dec 18 2017 *) -
PARI
x='x+O('x^30); Vec(-2*x*(12*x^2+4*x+1)/(8*x^3+4*x^2+2*x-1)) \\ G. C. Greubel, Dec 18 2017
Formula
a(n) = Trace of matrix [({2,2,2},{2,0,0},{0,2,0})^n].
a(n) = 2^n * Trace of matrix [({1,1,1},{1,0,0},{0,1,0})^n].
From Colin Barker, Sep 02 2013: (Start)
a(n) = 2*a(n-1) + 4*a(n-2) + 8*a(n-3).
G.f.: -2*x*(12*x^2+4*x+1)/(8*x^3+4*x^2+2*x-1). (End)
Extensions
More terms from Colin Barker, Sep 02 2013