A137213 - OEIS

%I #14 Sep 08 2022 08:45:32

%S 0,1,4,15,52,173,560,1779,5576,17305,53308,163287,497980,1513541,

%T 4587944,13878075,41910032,126395953,380795380,1146267039,3448170436,

%U 10367130845,31156000928,93599839107,281117798360,844121793481

%N First differences of A137212.

%H G. C. Greubel, <a href="/A137213/b137213.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-3).

%F From _R. J. Mathar_, Mar 17 2008: (Start)

%F O.g.f.: 1/(1-3*x) - 1/(1-2*x-x^2) = x*(1-x)/( (1-3*x)*(1-2*x-x^2) ).

%F a(n) = 3^n - A000129(n+1). (End)

%t LinearRecurrence[{5,-5,-3},{0,1,4},30] (* _Harvey P. Dale_, Apr 18 2019 *)

%o (Magma) [n le 3 select (n-1)^2 else 5*Self(n-1) -5*Self(n-2) -3*Self(n-3): n in [1..31]]; // _G. C. Greubel_, Jan 05 2022

%o (Sage) [3^n - lucas_number1(n+1,2,-1) for n in (0..30)] # _G. C. Greubel_, Jan 05 2022

%Y Cf. A000129, A132894, A137212.

%K nonn

%O 0,3

%A _Paul Curtz_, Mar 06 2008

%E More terms from _R. J. Mathar_, Mar 17 2008