A072260 a(n) = ((6*n+19)*4^n - 1)/3.

6, 33, 165, 789, 3669, 16725, 75093, 333141, 1463637, 6378837, 27612501, 118838613, 508908885, 2169853269, 9216283989, 39012619605, 164640413013, 692921390421, 2909124515157

Offset: 0

Author

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

Keywords

• nonn
• easy

Comments

Related to Collatz function (for n>0). 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).

Crossrefs

Cf. A072257, A072258, A072259.

Programs

GAP

List([0..20], n-> ((6*n+19)*4^n-1)/3); # G. C. Greubel, Jan 14 2020

Magma

[((6*n+19)*4^n-1)/3: n in [0..20]]; // G. C. Greubel, Jan 14 2020

Maple

seq( ((6*n+19)*4^n -1)/3, n=0..20); # G. C. Greubel, Jan 14 2020

Mathematica

LinearRecurrence[{9,-24,16}, {6,33,165}, 20] (* G. C. Greubel, Jan 14 2020 *)
Table[((6n+19)4^n-1)/3,{n,0,20}] (* Harvey P. Dale, Jun 20 2024 *)

PARI

a(n)=((6*n+19)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[((6*n+19)*4^n-1)/3 for n in (0..20)] # G. C. Greubel, Jan 14 2020

Formula

G.f.: 3*(2-7*x+4*x^2)/((1-x)*(1-4*x)^2). - Bruno Berselli, Dec 16 2011

E.g.f.: ((19 + 24*x)*exp(4*x) - exp(x))/3. - G. C. Greubel, Jan 14 2020

Extensions

Edited and extended by Henry Bottomley, Aug 06 2002