A139615 - OEIS

%I #20 Apr 04 2024 10:42:05

%S 15,120,225,330,435,540,645,750,855,960,1065,1170,1275,1380,1485,1590,

%T 1695,1800,1905,2010,2115,2220,2325,2430,2535,2640,2745,2850,2955,

%U 3060,3165,3270,3375,3480,3585,3690,3795,3900,4005,4110,4215

%N a(n) = 105*n + 15.

%C Numbers of the 15th column of positive numbers in the square array of nonnegative and polygonal numbers A139600. Also, numbers of the 15th column in the square array A057145.

%H Vincenzo Librandi, <a href="/A139615/b139615.txt">Table of n, a(n) for n = 0..5000</a>

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

%F From _Elmo R. Oliveira_, Apr 04 2024: (Start)

%F G.f.: 15*(1+6*x)/(x-1)^2.

%F E.g.f.: 15*exp(x)*(1 + 7*x).

%F a(n) = 15*A016993(n).

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

%t 105*Range[0,40]+15 (* or *) LinearRecurrence[{2,-1},{15,120},50] (* _Harvey P. Dale_, May 07 2016 *)

%o (Magma) [15*(7*n + 1): n in [0..60]]; // _Vincenzo Librandi_, Jul 23 2011

%o (PARI) a(n)=105*n+15 \\ _Charles R Greathouse IV_, Oct 05 2011

%Y Cf. A016993, A057145, A139600.

%K easy,nonn

%O 0,1

%A _Omar E. Pol_, Apr 27 2008