|
|
A153234
|
|
a(n) = floor(2^n/9).
|
|
8
|
|
|
0, 0, 0, 0, 1, 3, 7, 14, 28, 56, 113, 227, 455, 910, 1820, 3640, 7281, 14563, 29127, 58254, 116508, 233016, 466033, 932067, 1864135, 3728270, 7456540, 14913080, 29826161, 59652323, 119304647, 238609294, 477218588, 954437176, 1908874353, 3817748707, 7635497415, 15270994830
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) + a(n+3) = 2^n - 1 = A000225(n), n > 0.
a(n) = round((2*2^n-9)/18) = floor((2^n-1)/9) = ceiling((2^n-8)/9).
a(n) = a(n-6) + 7*2^(n-6), n > 5. (End)
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 3*a(n-4) - 2*a(n-5).
G.f.: x^4 / ( (1-2*x)*(1-x^2)*(1-x+x^2) ).
|
|
MAPLE
|
|
|
MATHEMATICA
|
|
|
PROG
|
(PARI) x='x+O('x^44); concat(vector(4), Vec(x^4/((x-1)*(2*x-1)*(1+x)*(x^2-x+1)))) \\ Altug Alkan, Mar 25 2016
(Sage) [floor(2^n/9) for n in (0..40)] # G. C. Greubel, Jun 05 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|