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a(n) = 14*n + 1.
4

%I #20 Apr 03 2024 15:15:59

%S 1,15,29,43,57,71,85,99,113,127,141,155,169,183,197,211,225,239,253,

%T 267,281,295,309,323,337,351,365,379,393,407,421,435,449,463,477,491,

%U 505,519,533,547,561,575,589,603,617,631,645,659,673,687,701,715,729

%N a(n) = 14*n + 1.

%C Left column of triangle A131876.

%C Binomial transform of (1, 14, 0, 0, 0, ...).

%C Partial sums give A051868. - _Leo Tavares_, Mar 19 2023

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

%F a(n) = 14*n + 1.

%F From _Elmo R. Oliveira_, Apr 03 2024: (Start)

%F G.f.: (1+13*x)/(1-x)^2.

%F E.g.f.: exp(x)*(1 + 14*x).

%F a(n) = A051868(n+1) - A051868(n).

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

%e a(2) = 29 = 2*14 + 1.

%e a(2) = 29 = (1, 2, 1) dot (1, 14, 0) = (1 + 28 + 0).

%t Range[1, 1000, 14] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)

%Y Cf. A008596, A131876.

%Y Cf. A051868.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Jul 22 2007