OFFSET
0,1
COMMENTS
Related to Collatz function (for n>0). All terms are 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*(4-17*x+12*x^2)/((1-x)*(1-4*x)^2). - Bruno Berselli, Dec 16 2011
E.g.f.: ((37 + 24*x)*exp(4*x) - exp(x))/3. - G. C. Greubel, Jan 14 2020
MAPLE
seq( ((6*n+37)*4^n -1)/3, n=0..30); # G. C. Greubel, Jan 14 2020
MATHEMATICA
LinearRecurrence[{9, -24, 16}, {12, 57, 261}, 30] (* Harvey P. Dale, Mar 10 2018 *)
PROG
(PARI) a(n)=((6*n+37)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [((6*n+37)*4^n -1)/3: n in [0..30]]; // G. C. Greubel, Jan 14 2020
(Sage) [((6*n+37)*4^n -1)/3 for n in (0..30)] # G. C. Greubel, Jan 14 2020
(GAP) List([0..30], n-> ((6*n+37)*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
More terms from Harvey P. Dale, Mar 10 2018
STATUS
approved