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 A169634 a(n) = 3*7^n. 12
 3, 21, 147, 1029, 7203, 50421, 352947, 2470629, 17294403, 121060821, 847425747, 5931980229, 41523861603, 290667031221, 2034669218547, 14242684529829, 99698791708803, 697891541961621, 4885240793731347, 34196685556119429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Essentially first differences of A120741. Binomial transform of A169604. Second binomial transform of A005053 without initial term 1. Inverse binomial transform of A103333 without initial term 1. Second inverse binomial transform of A013708. Except for first term 3, these are the integers that satisfy phi(n) = 4*n/7. - Michel Marcus, Jul 14 2015 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 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 Shalosh B. Ekhad and Doron Zeilberger, 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, arXiv:2103.12852 [math.CO], 2021. Richard P. Stanley, Some Linear Recurrences Motivated by Stern's Diatomic Array, arXiv:1901.04647 [math.CO], 2019. Also American Mathematical Monthly 127.2 (2020): 99-111. Index entries for linear recurrences with constant coefficients, signature (7). FORMULA a(n) = 7*a(n-1) for n > 0; a(0) = 3. G.f.: 3/(1-7*x). PROG (Magma) [ 3*7^n: n in [0..19] ]; CROSSREFS 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). Sequence in context: A173350 A323203 A372943 * A088088 A206638 A357652 Adjacent sequences: A169631 A169632 A169633 * A169635 A169636 A169637 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Apr 04 2010 STATUS approved

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Last modified May 20 13:50 EDT 2024. Contains 372716 sequences. (Running on oeis4.)