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%I #21 Jan 03 2024 08:44:14
%S 0,0,0,1,3,5,9,21,45,85,165,341,693,1365,2709,5461,10965,21845,43605,
%T 87381,174933,349525,698709,1398101,2796885,5592405,11183445,22369621,
%U 44741973,89478485,178951509,357913941,715838805,1431655765,2863289685,5726623061
%N a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4).
%H Vincenzo Librandi, <a href="/A136401/b136401.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,6,-4).
%F a(n+3) = Sum_{k=0..n} A154957(n,k)*2^k. - _Philippe Deléham_, Mar 21 2014
%F G.f.: x^3/((x-1)*(2*x-1)*(2*x^2+1)). - _Philippe Deléham_, Mar 21 2014
%e Binary.................Decimal
%e 0............................0
%e 0............................0
%e 0............................0
%e 1............................1
%e 11...........................3
%e 101..........................5
%e 1001.........................9
%e 10101.......................21
%e 101101......................45
%e 1010101.....................85
%e 10100101...................165
%e 101010101..................341
%e 1010110101.................693
%e 10101010101...............1365
%e 101010010101..............2709
%e 1010101010101.............5461
%e 10101011010101...........10965
%e 101010101010101..........21845
%e 1010101001010101.........43605, etc. - _Philippe Deléham_, Mar 21 2014
%t CoefficientList[Series[x^3/((x - 1) (2 x - 1) (2 x^2 + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Mar 22 2014 *)
%t LinearRecurrence[{3,-4,6,-4},{0,0,0,1},40] (* _Harvey P. Dale_, Mar 13 2018 *)
%Y Cf. A154957.
%K nonn,easy
%O 0,5
%A _Paul Curtz_, Mar 30 2008
%E More terms from _Philippe Deléham_, Mar 21 2014
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