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

0,1

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).

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

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 *)

Prog

(PARI) a(n)=((6*n+37)*4^n-1)/3 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [((6*n+37)*4^n -1)/3: n in [0..30]]; // G. C. Greubel, Jan 14 2020
(Sage) [((6*n+37)*4^n -1)/3 for n in (0..30)] # G. C. Greubel, Jan 14 2020
(GAP) List([0..30], n-> ((6*n+37)*4^n -1)/3); # G. C. Greubel, Jan 14 2020

Crossrefs

Cf. A072257, A072258, A072260.

Sequence in context: A212065 A121693 A190297 * A272233 A283164 A242983

Adjacent sequences: A072256 A072257 A072258 * A072260 A072261 A072262

Keyword

nonn,easy

Author

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

Extensions

Edited and extended by Henry Bottomley, Aug 06 2002

More terms from Harvey P. Dale, Mar 10 2018

Status

approved