OFFSET
0,2
COMMENTS
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
KEYWORD
nonn,easy
AUTHOR
Brad Clardy, May 03 2012
STATUS
approved