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

Author

Brad Clardy, May 03 2012

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A015521, A112627.

Programs

Magma

[(1/5)*2^(4*i) -(1/5): i in [0..30]];

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 *)

PARI

a(n) = (16^n - 1)/5; \\ Michel Marcus, Jan 22 2016

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