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A127221
a(n) = 2^n*pentanacci(n) or (2^n)*A023424(n-1).
3
2, 12, 56, 240, 992, 3648, 14464, 57088, 224768, 883712, 3471360, 13651968, 53682176, 211075072, 829915136, 3263102976, 12830244864, 50447253504, 198353354752, 779904614400, 3066503888896, 12057176965120, 47407572189184, 186401664532480, 732912043425792
OFFSET
1,1
FORMULA
a(n) = Trace of matrix [({2,2,2,2,2},{2,0,0,0,0},{0,2,0,0,0},{0,0,2,0,0},{0,0,0,2,0})^n].
a(n) = 2^n * Trace of matrix [({1,1,1,1,1},{1,0,0,0,0},{0,1,0,0,0},{0,0,1,0,0},{0,0,0,1,0})^n].
G.f.: -2*x*(1 +4*x +12*x^2 +32*x^3 +80*x^4)/(-1 +2*x +4*x^2 +8*x^3 +16*x^4 +32*x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; corrected by R. J. Mathar, Sep 16 2009
a(n) = 2*a(n-1)+4*a(n-2)+8*a(n-3)+16*a(n-4)+32*a(n-5). - Colin Barker, Sep 02 2013
MATHEMATICA
Table[Tr[MatrixPower[2*{{1, 1, 1, 1, 1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, x]], {x, 1, 20}]
LinearRecurrence[{2, 4, 8, 16, 32}, {2, 12, 56, 240, 992}, 50] (* G. C. Greubel, Dec 19 2017 *)
PROG
(PARI) x='x+O('x^30); Vec(-2*x*(1 +4*x +12*x^2 +32*x^3 +80*x^4)/(-1 +2*x +4*x^2 +8*x^3 +16*x^4 +32*x^5)) \\ G. C. Greubel, Dec 19 2017
(Magma) I:=[2, 12, 56, 240, 992]; [n le 5 select I[n] else 2*Self(n-1) + 4*Self(n-2) + 8*Self(n-3) + 16*Self(n-4) + 32*Self(n-5): n in [1..30]]; // G. C. Greubel, Dec 19 2017
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Jan 09 2007
EXTENSIONS
Definition corrected by R. J. Mathar, Sep 17 2009
More terms from Colin Barker, Sep 02 2013
STATUS
approved