|
|
|
|
2, 2, 6, 14, 38, 112, 276, 814, 1998, 5702, 14226, 39404, 99908, 270922, 695106, 1859134, 4807518, 12748472, 33128916, 87394454, 227792678, 599050102, 1564242906, 4106054164, 10733283588, 28143585362, 73614464826, 192899714414, 504751433798, 1322156172352
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
Sum of the binomial and inverse binomial transforms of A014217.
Starting at a(1), the last digits form a period-4 sequence 2, 6, 4, 8.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = +2*a(n-1) +7*a(n-2) -12*a(n-3) -11*a(n-4) +16*a(n-5) -4*a(n-6), n>6. - R. J. Mathar, Jun 14 2010
G.f.: 2*(1-x-6*x^2+6*x^3+7*x^4-2*x^6)/((1-2*x)*(1+2*x)*(1+x-x^2)*(1-3*x+x^2)). - Colin Barker, Aug 13 2012
a(n) = (-1)^n*LucasL(n) + LucasL(2*n) - (1 + (-1)^n)*2^(n-1) - [n=0]. - G. C. Greubel, Oct 26 2022
|
|
MATHEMATICA
|
Join[{2}, LinearRecurrence[{2, 7, -12, -11, 16, -4}, {2, 6, 14, 38, 112, 276}, 30]] (* Harvey P. Dale, Nov 25 2013 *)
|
|
PROG
|
(Magma) [n eq 0 select 2 else (-1)^n*Lucas(n) +Lucas(2*n) -(1+(-1)^n)*2^(n-1): n in [0..50]]; // G. C. Greubel, Oct 26 2022
(SageMath)
def A142710(n): return (-1)^n*lucas_number2(n, 1, -1) + lucas_number2(2*n, 1, -1) - (1 + (-1)^n)*2^(n-1) -int(n==0)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|