A169634 a(n) = 3*7^n.

3, 21, 147, 1029, 7203, 50421, 352947, 2470629, 17294403, 121060821, 847425747, 5931980229, 41523861603, 290667031221, 2034669218547, 14242684529829, 99698791708803, 697891541961621, 4885240793731347, 34196685556119429, 239376798892836003, 1675637592249852021

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).

Mathematica

3*7^Range[0, 25] (* Paolo Xausa, Jan 17 2025 *)

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