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a(n) = 10*2^n - 3*A083658(n+2).
2

%I #17 Jun 21 2016 02:41:48

%S 1,5,13,35,79,185,397,875,1831,3905,8053,16835,34399,70985,144157,

%T 294875,596311,1212305,2444293,4947635,9954319,20085785,40348717,

%U 81228875,162989191,327572705,656739733,1318262435,2641307839,5296964585,10608278077,21259602875

%N a(n) = 10*2^n - 3*A083658(n+2).

%C The sequence can be defined as the row sums of the triangle T(n,k)

%C .1;

%C .3,.2;

%C .3,.6,.4;

%C .9,.6,12,.8;

%C .9,18,12,24,16;

%C 27,18,36,24,48,32;

%C with left column A162436, diagonal the powers of 2, and the recurrence T(n+2,k) = 3*T(n,k).

%H G. C. Greubel, <a href="/A167710/b167710.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 (2,3,-6).

%F a(n+1) - 2*a(n) = A162436(n+2).

%F a(n) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3).

%F G.f.: (1+3*x)/((2*x-1) * (3*x^2-1)). - _R. J. Mathar_, Feb 27 2010

%t LinearRecurrence[{2,3,-6},{1,5,13},40] (* _Harvey P. Dale_, Oct 03 2014 *)

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Nov 10 2009

%E Replaced cross-references by link to the index - _R. J. Mathar_, Feb 27 2010