%I #31 Apr 16 2024 07:08:23

%S 16,34,52,70,88,106,124,142,160,178,196,214,232,250,268,286,304,322,

%T 340,358,376,394,412,430,448,466,484,502,520,538,556,574,592,610,628,

%U 646,664,682,700,718,736,754,772,790,808,826,844,862,880,898,916,934,952,970

%N a(n) = 18*n + 16.

%C Sixth column of A006370 (the Collatz or 3x+1 map) when it is interpreted as a rectangular array with six columns read by rows.

%H Leo Tavares, <a href="/A350522/a350522.jpg">Illustration: Triple Hexagonal Rings</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = A239129(n+1) - 1.

%F From _Stefano Spezia_, Jan 04 2022: (Start)

%F O.g.f.: 2*(8 + x)/(1 - x)^2.

%F E.g.f.: 2*exp(x)*(8 + 9*x).

%F a(n) = 2*a(n-1) - a(n-2) for n > 1. (End)

%F a(n) = 3*A008588(n+1) - 2. - _Leo Tavares_, Sep 14 2022

%F From _Elmo R. Oliveira_, Apr 12 2024: (Start)

%F a(n) = 2*A017257(n) = A006370(A016969(n)).

%F a(n) = 2*(A062728(n+1) - A062728(n)). (End)

%p seq(18*n+16, n=0..53);

%t Table[18n+16, {n, 0, 53}]

%o (PARI) a(n)=18*n+16

%o (Magma) [18*n+16: n in [0..53]];

%o (Maxima) makelist(18*n+16, n, 0, 53);

%o (GAP) List([0..53], n-> 18*n+16)

%o (Python) [18*n+16 for n in range(53)]

%Y Bisection of A017245.

%Y Cf. A006370, A008588, A008600, A016969, A017257, A062728, A239129.

%K nonn,easy

%O 0,1

%A _Omar E. Pol_, Jan 03 2022