A133455 a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3), with a(0) = 4, a(1) = 2, a(2) = 1.
4, 2, 1, 5, 16, 35, 67, 128, 253, 509, 1024, 2051, 4099, 8192, 16381, 32765, 65536, 131075, 262147, 524288, 1048573, 2097149, 4194304, 8388611, 16777219, 33554432, 67108861, 134217725, 268435456, 536870915, 1073741827, 2147483648, 4294967293, 8589934589, 17179869184
Offset: 0
Keywords
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,2).
Programs
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Magma
a:=[4,2,1]; [n le 3 select a[n] else 3*Self(n-1) -3*Self(n-2)+2*Self(n-3):n in [1..35]]; // Marius A. Burtea, Jan 03 2020
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Magma
R
:=PowerSeriesRing(Integers(), 35); Coefficients(R!( (4 - 10*x + 7*x^2)/((1 - 2*x)*(1 - x + x^2)))); // Marius A. Burtea, Jan 03 2020 -
Mathematica
LinearRecurrence[{3, -3, 2},{4, 2, 1},15] (* Ray Chandler, Sep 23 2015 *) -
PARI
Vec((4 - 10*x + 7*x^2)/((1 - 2*x)*(1 - x + x^2)) + O(x^40)) \\ Andrew Howroyd, Jan 03 2020
Formula
a(n)-2^n = hexaperiodic 3, 0, -3, -3, 0, 3.
O.g.f: -(4 - 10*x + 7*x^2)/((2*x - 1)*(x^2 - x + 1)). - R. J. Mathar, Nov 30 2007
a(n) = 2^n + 3*A010892(n+1). - R. J. Mathar, Jul 20 2009
a(n) = (-1)^n*A146321(n + 1). - Andrew Howroyd, Jan 03 2020
Extensions
Terms a(15) and beyond from Andrew Howroyd, Jan 03 2020
Comments