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%I #55 Feb 28 2024 12:42:54
%S 0,3,51,819,13107,209715,3355443,53687091,858993459,13743895347,
%T 219902325555,3518437208883,56294995342131,900719925474099,
%U 14411518807585587,230584300921369395,3689348814741910323,59029581035870565171,944473296573929042739
%N a(n) = (16^n - 1)/5.
%C Even bisection of A015521 and also A112627. All of the terms are divisible by 3, even terms by 17.
%C These are binary numbers 11, 110011, 1100110011, ... - _Jamie Simpson_, Oct 28 2022
%H Robert Israel, <a href="/A182512/b182512.txt">Table of n, a(n) for n = 0..830</a>
%H E. Estrada and J. A. de la Pena, <a href="http://arxiv.org/abs/1302.1176">From Integer Sequences to Block Designs via Counting Walks in Graphs</a>, arXiv preprint arXiv:1302.1176 [math.CO], 2013. - From _N. J. A. Sloane_, Feb 28 2013
%H E. Estrada and J. A. de la Pena, <a href="http://www.nntdm.net/papers/nntdm-19/NNTDM-19-3-78-84.pdf">Integer sequences from walks in graphs</a>, Notes on Number Theory and Discrete Mathematics, Vol. 19, 2013, No. 3, 78-84
%H Andreas M. Hinz and Paul K. Stockmeyer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Hinz/hinz5.html">Precious Metal Sequences and Sierpinski-Type Graphs</a>, J. Integer Seq., Vol 25 (2022), Article 22.4.8.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F a(n) = 16*a(n-1) + 3 where a(0)=0.
%F a(n) = A015521(2n).
%F a(n) = A112627(2n) for n >= 1; a(0)=0.
%F G.f.: 3*x / ( (16*x-1)*(x-1) ). - _R. J. Mathar_, Apr 20 2015
%F a(n) = 3*A131865(n-1). - _R. J. Mathar_, Apr 20 2015
%F a(n) = A108020(n)/4. - _Jamie Simpson_, Oct 28 2022
%p seq((16^n-1)/5, n=0..50); # _Robert Israel_, Jan 22 2016
%t (16^Range[0,20]-1)/5 (* _Harvey P. Dale_, Aug 07 2019 *)
%t LinearRecurrence[{17,-16},{0,3},20] (* _Harvey P. Dale_, Aug 07 2019 *)
%o (Magma)[(1/5)*2^(4*i) -(1/5): i in [0..30]];
%o (PARI) a(n) = (16^n - 1)/5; \\ _Michel Marcus_, Jan 22 2016
%Y Cf. A015521, A112627.
%K nonn,easy
%O 0,2
%A _Brad Clardy_, May 03 2012
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