A127216 a(n) = 2^n*tetranacci(n) or (2^n)*A001648(n).

2, 12, 56, 240, 832, 3264, 12672, 48896, 187904, 724992, 2795520, 10776576, 41541632, 160153600, 617414656, 2380201984, 9175957504, 35374497792, 136373075968, 525735034880, 2026773676032, 7813464064000, 30121872326656, 116123550875648, 447670682386432

Offset

1,1

Links

Indranil Ghosh, Table of n, a(n) for n = 1..1702

Index entries for linear recurrences with constant coefficients, signature (2,4,8,16).

Formula

a(n) = Trace of matrix [({{2,2,2,2},{2,0,0,0},{0,2,0,0),{0,0,2,0}})^n] a(n) = 2^n Trace of matrix [({{1,1,1,1},{1,0,0,0},{0,1,0,0},{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) + 16*a(n-4).

G.f.: -2*x*(32*x^3+12*x^2+4*x+1) / (16*x^4+8*x^3+4*x^2+2*x-1). (End)

Example

a(8) = (2^8) * A001648(8) = 256 * 191  = 48896. - Indranil Ghosh, Feb 09 2017

Mathematica

Table[Tr[MatrixPower[2*{{1, 1, 1, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}}, x]], {x, 1, 20}]
LinearRecurrence[{2, 4, 8, 16}, {2, 12, 56, 240}, 50] (* G. C. Greubel, Dec 19 2017 *)

Prog

(PARI) x='x+O('x^30); Vec(-2*x*(32*x^3+12*x^2+4*x+1)/(16*x^4 +8*x^3 +4*x^2 +2*x -1)) \\ G. C. Greubel, Dec 19 2017
(Magma) I:=[2, 12, 56, 240]; [n le 4 select I[n] else 2*Self(n-1) + 4*Self(n-2) + 8*Self(n-3) + 16*Self(n-4): n in [1..30]]; // G. C. Greubel, Dec 19 2017

Crossrefs

Cf. A087131, A127210, A127211, A127212, A127213, A127214, A127216, A001648.

Sequence in context: A124723 A122229 A285146 * A006659 A194771 A127221

Adjacent sequences: A127213 A127214 A127215 * A127217 A127218 A127219

Keyword

nonn,easy

Author

Artur Jasinski, Jan 09 2007

Extensions

More terms from Colin Barker, Sep 02 2013

Status

approved