A072259 a(n) = ((6*n+37)*4^n - 1)/3.

12, 57, 261, 1173, 5205, 22869, 99669, 431445, 1856853, 7951701, 33903957, 144004437, 609572181, 2572506453, 10826896725, 45455070549, 190410216789, 796000605525, 3321441375573, 13835521316181, 57541108520277, 238960527103317, 991026480502101

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

• 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, A072258, A072260.

Programs

GAP

List([0..30], n-> ((6*n+37)*4^n -1)/3); # G. C. Greubel, Jan 14 2020

Magma

[((6*n+37)*4^n -1)/3: n in [0..30]]; // 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 *)

PARI

a(n)=((6*n+37)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015

Sage

[((6*n+37)*4^n -1)/3 for n in (0..30)] # G. C. Greubel, Jan 14 2020

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

Extensions

Edited and extended by Henry Bottomley, Aug 06 2002

More terms from Harvey P. Dale, Mar 10 2018