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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Mar 30 2008
EXTENSIONS
More terms from Philippe Deléham, Mar 21 2014
STATUS
approved