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

Author

N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A072257, A072259, A072260.

Programs

GAP

List([0..40], n-> ((6*n+1)*4^n -1)/3); # G. C. Greubel, Jan 14 2020

Magma

[((6*n+1)*4^n -1)/3: n in [0..40]]; // 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 *)

PARI

a(n)=((6*n+1)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[((6*n+1)*4^n -1)/3 for n in (0..40)] # G. C. Greubel, Jan 14 2020

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

Extensions

Edited and extended by Henry Bottomley, Aug 06 2002