A199923 a(n) = Sum_{k=0..3^(n-1)} gcd(k,3^(n-1)) for n > 0 and a(0) = 1.

1, 2, 8, 30, 108, 378, 1296, 4374, 14580, 48114, 157464, 511758, 1653372, 5314410, 17006112, 54206982, 172186884, 545258466, 1721868840, 5423886846, 17046501516, 53464027482, 167365651248, 523017660150, 1631815099668, 5083731656658, 15816054042936

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-9).

Formula

a(n) = 2 * (n+2) * 3^(n-2), n > 0. - Sean A. Irvine, Jun 27 2022

From G. C. Greubel, Nov 24 2023: (Start)

a(n) = (2*(n+2)*3^n + 5*[n=0])/9.

G.f.: (9 - 6*x))/(9*(1 - 3*x)^2).

E.g.f.: (1/9)*( 5 + 2*(2 + 3*x)*exp(3*x) ). (End)

Example

a(3) = 9 + 1 + 1 + 3 + 1 + 1 + 3 + 1 + 1 + 9.

Mathematica

LinearRecurrence[{6, -9}, {1, 2, 8}, 41] (* G. C. Greubel, Nov 24 2023 *)

Prog

(Magma) [1] cat [n le 2 select 2^(2*n-1) else 6*Self(n-1) -9*Self(n-2): n in [1..40]]; // G. C. Greubel, Nov 24 2023
(SageMath) [(2*(n+2)*3^n + 5*int(n==0))//9 for n in range(41)] # G. C. Greubel, Nov 24 2023

Crossrefs

First differences of A086972.

Row sums of A199922.

Sequence in context: A365693 A168605 A127865 * A230269 A278023 A077839

Adjacent sequences: A199920 A199921 A199922 * A199924 A199925 A199926

Keyword

nonn

Author

Peter Luschny, Nov 12 2011

Extensions

More terms from Sean A. Irvine, Jun 27 2022

Status

approved