A072257 a(n) = ((6*n-17)*4^n - 1)/3.

-6, -15, -27, 21, 597, 4437, 25941, 136533, 677205, 3233109, 15029589, 68506965, 307582293, 1364546901, 5995058517, 26127717717, 113100805461, 486762960213, 2084490794325, 8887718991189

Offset: 0

Author

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

Keywords

• sign
• easy

Comments

Related to Collatz function (for n>2). 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. A072258, A072259, A072260.

Programs

GAP

List([0..40], n-> ((6*n-17)*4^n -1)/3); # G. C. Greubel, Jan 14 2020

Magma

[((6*n-17)*4^n -1)/3: n in [0..40]]; // G. C. Greubel, Jan 14 2020

Maple

seq( ((6*n-17)*4^n -1)/3, n=0..40); # G. C. Greubel, Jan 14 2020

Mathematica

LinearRecurrence[{9,-24,16},{-6,-15,-27},40] (* Harvey P. Dale, Nov 23 2015 *)

PARI

a(n)=((6*n-17)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[((6*n-17)*4^n -1)/3 for n in (0..40)] # G. C. Greubel, Jan 14 2020

Formula

G.f.: -3*(2-13*x+12*x^2)/((1-x)*(1-4*x)^2). - Bruno Berselli, Dec 16 2011

E.g.f.: (-1/3)*( (17-24*x)*exp(4*x) + exp(x) ). - G. C. Greubel, Jan 14 2020

Extensions

Edited and extended by Henry Bottomley, Aug 06 2002