A182512 a(n) = (16^n - 1)/5.

0, 3, 51, 819, 13107, 209715, 3355443, 53687091, 858993459, 13743895347, 219902325555, 3518437208883, 56294995342131, 900719925474099, 14411518807585587, 230584300921369395, 3689348814741910323, 59029581035870565171, 944473296573929042739

Offset

0,2

Comments

Even bisection of A015521 and also A112627. All of the terms are divisible by 3, even terms by 17.

These are binary numbers 11, 110011, 1100110011, ... - Jamie Simpson, Oct 28 2022

Links

Robert Israel, Table of n, a(n) for n = 0..830

E. Estrada and J. A. de la Pena, From Integer Sequences to Block Designs via Counting Walks in Graphs, arXiv preprint arXiv:1302.1176 [math.CO], 2013. - From N. J. A. Sloane, Feb 28 2013

E. Estrada and J. A. de la Pena, Integer sequences from walks in graphs, Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 3, 78-84

Andreas M. Hinz and Paul K. Stockmeyer, Precious Metal Sequences and Sierpinski-Type Graphs, J. Integer Seq., Vol 25 (2022), Article 22.4.8.

Index entries for linear recurrences with constant coefficients, signature (17,-16).

Formula

a(n) = 16*a(n-1) + 3 where a(0)=0.

a(n) = A015521(2n).

a(n) = A112627(2n) for n >= 1; a(0)=0.

G.f.: 3*x / ( (16*x-1)*(x-1) ). - R. J. Mathar, Apr 20 2015

a(n) = 3*A131865(n-1). - R. J. Mathar, Apr 20 2015

a(n) = A108020(n)/4. - Jamie Simpson, Oct 28 2022

Maple

seq((16^n-1)/5, n=0..50); # Robert Israel, Jan 22 2016

Mathematica

(16^Range[0, 20]-1)/5 (* Harvey P. Dale, Aug 07 2019 *)
LinearRecurrence[{17, -16}, {0, 3}, 20] (* Harvey P. Dale, Aug 07 2019 *)

Prog

(Magma)[(1/5)*2^(4*i) -(1/5): i in [0..30]];
(PARI) a(n) = (16^n - 1)/5; \\ Michel Marcus, Jan 22 2016

Crossrefs

Cf. A015521, A112627.

Sequence in context: A232453 A248341 A145242 * A378552 A075869 A361051

Adjacent sequences: A182509 A182510 A182511 * A182513 A182514 A182515

Keyword

nonn,easy

Author

Brad Clardy, May 03 2012

Status

approved