A136401 a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4), with initial terms 0,0,0,1.
0, 0, 0, 1, 3, 5, 9, 21, 45, 85, 165, 341, 693, 1365, 2709, 5461, 10965, 21845, 43605, 87381, 174933, 349525, 698709, 1398101, 2796885, 5592405, 11183445, 22369621, 44741973, 89478485, 178951509, 357913941, 715838805, 1431655765, 2863289685, 5726623061
Offset: 0
Examples
Binary.................Decimal 0............................0 0............................0 0............................0 1............................1 11...........................3 101..........................5 1001.........................9 10101.......................21 101101......................45 1010101.....................85 10100101...................165 101010101..................341 1010110101.................693 10101010101...............1365 101010010101..............2709 1010101010101.............5461 10101011010101...........10965 101010101010101..........21845 1010101001010101.........43605, etc. - _Philippe Deléham_, Mar 21 2014
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-4,6,-4).
Crossrefs
Cf. A154957.
Programs
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Mathematica
CoefficientList[Series[x^3/((x - 1) (2 x - 1) (2 x^2 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 22 2014 *) LinearRecurrence[{3,-4,6,-4},{0,0,0,1},40] (* Harvey P. Dale, Mar 13 2018 *)
Formula
a(n+3) = Sum_{k=0..n} A154957(n,k)*2^k. - Philippe Deléham, Mar 21 2014
G.f.: x^3/((x-1)*(2*x-1)*(2*x^2+1)). - Philippe Deléham, Mar 21 2014
Extensions
More terms from Philippe Deléham, Mar 21 2014