OFFSET
0,1
COMMENTS
Related to Collatz function (for n>2). All terms are divisible by 3.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-24,16).
FORMULA
G.f.: -3*(2-13*x+12*x^2)/((1-x)*(1-4*x)^2). - Bruno Berselli, Dec 16 2011
E.g.f.: (-1/3)*( (17-24*x)*exp(4*x) + exp(x) ). - G. C. Greubel, Jan 14 2020
MAPLE
seq( ((6*n-17)*4^n -1)/3, n=0..40); # G. C. Greubel, Jan 14 2020
MATHEMATICA
LinearRecurrence[{9, -24, 16}, {-6, -15, -27}, 40] (* Harvey P. Dale, Nov 23 2015 *)
PROG
(PARI) a(n)=((6*n-17)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [((6*n-17)*4^n -1)/3: n in [0..40]]; // G. C. Greubel, Jan 14 2020
(Sage) [((6*n-17)*4^n -1)/3 for n in (0..40)] # G. C. Greubel, Jan 14 2020
(GAP) List([0..40], n-> ((6*n-17)*4^n -1)/3); # G. C. Greubel, Jan 14 2020
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
EXTENSIONS
Edited and extended by Henry Bottomley, Aug 06 2002
STATUS
approved