A123016 a(1)=1, a(2)=1, a(3)=4, a(4)=0; a(n)=12a(n-2)-16a(n-3) for n>=5.

1, 1, 4, 0, 32, -64, 384, -1280, 5632, -21504, 88064, -348160, 1400832, -5586944, 22380544, -89456640, 357957632, -1431568384, 5726797824, -22906142720, 91626668032, -366502477824, 1466018299904, -5864056422400, 23456259244032, -93824969867264, 375300013686784

Offset

1,3

Links

Table of n, a(n) for n=1..27.

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

Formula

G.f.: (-2*x^3 + 3*x^2 + x)/((1-2x) * (1+4x)). - Ralf Stephan, Jul 14 2013

a(n) = (16*2^n - (-4)^n)/48, n>0. - Ralf Stephan, Jul 18 2013

Maple

a[1]:=1: a[2]:=1: a[3]:=4: a[4]:=0: for n from 5 to 27 do a[n]:=12*a[n-2]-16*a[n-3] od: seq(a[n], n=1..27);

Mathematica

M = {{1, -1, -1, 1}, {-1, 1, -1, 1}, {-1, -1, 1, 1}, {1, 1, 1, -3}}; v[1] = {1, 0, 0, 0}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
LinearRecurrence[{-2, 8}, {1, 1, 4}, 30] (* Harvey P. Dale, Apr 23 2015 *)

Crossrefs

Sequence in context: A270933 A270293 A270900 * A231038 A271280 A271086

Adjacent sequences: A123013 A123014 A123015 * A123017 A123018 A123019

Keyword

sign,easy

Author

Roger L. Bagula, Sep 23 2006

Extensions

Edited by N. J. A. Sloane, Oct 08 2006

Status

approved