%I #23 Feb 25 2023 17:24:18
%S 3,21,147,1029,7203,50421,352947,2470629,17294403,121060821,847425747,
%T 5931980229,41523861603,290667031221,2034669218547,14242684529829,
%U 99698791708803,697891541961621,4885240793731347,34196685556119429
%N a(n) = 3*7^n.
%C Essentially first differences of A120741.
%C Binomial transform of A169604.
%C Second binomial transform of A005053 without initial term 1.
%C Inverse binomial transform of A103333 without initial term 1.
%C Second inverse binomial transform of A013708.
%C Except for first term 3, these are the integers that satisfy phi(n) = 4*n/7. - _Michel Marcus_, Jul 14 2015
%C Number of distinct quadratic residues (QR) over Z_7^n such that gcd(QR, 7^n) = 1 where n >= 1. - _Param Mayurkumar Parekh_, Feb 11 2023
%H Vincenzo Librandi, <a href="/A169634/b169634.txt">Table of n, a(n) for n = 0..300</a>
%H Shalosh B. Ekhad and Doron Zeilberger, <a href="https://arxiv.org/abs/2103.12852">A Bijective Proof of Richard Stanley's Observation that the sum of the cubes of the n-th row of Stern's Diatomic array equals 3 times 7 to the power n-1</a>, arXiv:2103.12852 [math.CO], 2021.
%H Richard P. Stanley, <a href="https://arxiv.org/abs/1901.04647">Some Linear Recurrences Motivated by Stern's Diatomic Array</a>, arXiv:1901.04647 [math.CO], 2019. Also American Mathematical Monthly 127.2 (2020): 99-111.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (7).
%F a(n) = 7*a(n-1) for n > 0; a(0) = 3.
%F G.f.: 3/(1-7*x).
%o (Magma) [ 3*7^n: n in [0..19] ];
%Y Cf. A120741, A169604 (3*6^n), A005053 (expand (1-2x)/(1-5x)), A103333 (expand (1-5x)/(1-8x)), A013708 (3^(2*n+1)), A007283 (3*2^n), A164346 (3*4^n).
%K nonn,easy
%O 0,1
%A _Klaus Brockhaus_, Apr 04 2010
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