A136299 - OEIS

%I #9 Apr 13 2021 01:36:36

%S 1,2,4,7,13,23,41,71,121,199,313,455,569,455,-455,-3641,-12743,-36409,

%T -94663,-233017,-553415,-1281593,-2912711,-6524473,-14447047,

%U -31690297,-68972999,-149130809,-320631239,-686001721,-1461481927,-3101920825,-6561755591,-13839339065

%N a(n) = 3*a(n-1) - 4*a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=7.

%H G. C. Greubel, <a href="/A136299/b136299.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 (3,0,-4).

%F From _R. J. Mathar_, Apr 04 2008: (Start)

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

%F a(n) = (11*2^n + (-1)^n)/9 - A001787(n+1)/12 if n>0. (End)

%F From _G. C. Greubel_, Apr 12 2021: (Start)

%F a(n) = (2^(n-2)*(41-3*n) + (-1)^n)/9 - (1/4)*[n=0].

%F E.g.f.: (-9 + 4*exp(-x) + (41 - 6*x)*exp(2*x))/36. (End)

%t LinearRecurrence[{3,0,-4}, {1,2,4,7}, 41] (* _G. C. Greubel_, Apr 12 2021 *)

%o (Magma) [1] cat [(2^(n-2)*(41-3*n) + (-1)^n)/9: n in [1..40]]; // _G. C. Greubel_, Apr 12 2021

%o (Sage) [1]+[(2^(n-2)*(41-3*n) + (-1)^n)/9 for n in (1..40)] # _G. C. Greubel_, Apr 12 2021

%Y Cf. A001787, A051013.

%K sign,easy

%O 0,2

%A _Paul Curtz_, Mar 22 2008