A072258 a(n) = ((6*n+1)*4^n - 1)/3.

0, 9, 69, 405, 2133, 10581, 50517, 234837, 1070421, 4805973, 21321045, 93672789, 408245589, 1767200085, 7605671253, 32570168661, 138870609237, 589842175317, 2496807654741, 10536986432853

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

Cf. A072257, A072259, A072260.

Sequence in context: A193698 A188800 A297393 * A196490 A297593 A198691

Adjacent sequences: A072255 A072256 A072257 * A072259 A072260 A072261

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