|
%I #20 Sep 08 2022 08:45:31
%S 4,2,1,5,16,35,67,128,253,509,1024,2051,4099,8192,16381,32765,65536,
%T 131075,262147,524288,1048573,2097149,4194304,8388611,16777219,
%U 33554432,67108861,134217725,268435456,536870915,1073741827,2147483648,4294967293,8589934589,17179869184
%N a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).
%C Sequence is identical to its third differences.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2).
%F a(n)-2^n = hexaperiodic 3, 0, -3, -3, 0, 3.
%F O.g.f: -(4 - 10*x + 7*x^2)/((2*x - 1)*(x^2 - x + 1)). - _R. J. Mathar_, Nov 30 2007
%F a(n) = 2^n + 3*A010892(n+1). - _R. J. Mathar_, Jul 20 2009
%F a(n) = (-1)^n*A146321(n + 1). - _Andrew Howroyd_, Jan 03 2020
%t LinearRecurrence[{3, -3, 2},{4, 2, 1},15] (* _Ray Chandler_, Sep 23 2015 *)
%o (PARI) Vec((4 - 10*x + 7*x^2)/((1 - 2*x)*(1 - x + x^2)) + O(x^40)) \\ _Andrew Howroyd_, Jan 03 2020
%o (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
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( (4 - 10*x + 7*x^2)/((1 - 2*x)*(1 - x + x^2)))); // _Marius A. Burtea_, Jan 03 2020
%Y Cf. A010892, A146321.
%K nonn
%O 0,1
%A _Paul Curtz_, Nov 27 2007
%E Terms a(15) and beyond from _Andrew Howroyd_, Jan 03 2020
|
