OFFSET
0,2
COMMENTS
Related to Collatz function (for n>0). All divisible by 3.
LINKS
G. C. Greubel, 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*x*(3-4*x)/((1-x)*(1-4*x)^2). - Bruno Berselli, Dec 16 2011
E.g.f.: ( (1 + 24*x)*exp(4*x) - exp(x) )/3. - G. C. Greubel, Jan 14 2020
MAPLE
seq( ((6*n+1)*4^n -1)/3, n=0..40); # G. C. Greubel, Jan 14 2020
MATHEMATICA
LinearRecurrence[{9, -24, 16}, {0, 9, 69}, 40] (* G. C. Greubel, Jan 14 2020 *)
PROG
(PARI) a(n)=((6*n+1)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [((6*n+1)*4^n -1)/3: n in [0..40]]; // G. C. Greubel, Jan 14 2020
(Sage) [((6*n+1)*4^n -1)/3 for n in (0..40)] # G. C. Greubel, Jan 14 2020
(GAP) List([0..40], n-> ((6*n+1)*4^n -1)/3); # G. C. Greubel, Jan 14 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
EXTENSIONS
Edited and extended by Henry Bottomley, Aug 06 2002
STATUS
approved