A136401 a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4).

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

0,5

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).

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

Example

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

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 *)

Crossrefs

Cf. A154957.

Sequence in context: A050355 A147039 A069927 * A147758 A129787 A328525

Adjacent sequences: A136398 A136399 A136400 * A136402 A136403 A136404

Keyword

nonn,easy

Author

Paul Curtz, Mar 30 2008

Extensions

More terms from Philippe Deléham, Mar 21 2014

Status

approved