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%I #22 Sep 08 2022 08:44:49
%S 1,5,14,35,81,180,389,825,1726,3575,7349,15020,30561,61965,125294,
%T 252795,509161,1024100,2057549,4130225,8284926,16609455,33282989,
%U 66669660,133507081,267285605,535010414,1070731475,2142612801
%N a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A027960.
%H G. C. Greubel, <a href="/A027974/b027974.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,-1,-2).
%F a(n) = 8*2^n - Fibonacci(n+5) - Fibonacci(n+3).
%F a(n) = A101220(4, 2, n+1).
%F G.f.: (1+2*x)/((1-2*x)*(1-x-x^2)). - _R. J. Mathar_, Sep 22 2008
%p with(combinat); f:=fibonacci; seq(2^(n+3) - f(n+5) - f(n+3), n=0..30); # _G. C. Greubel_, Sep 26 2019
%t Table[2^(n+3) - LucasL[n+4], {n,0,30}] (* _G. C. Greubel_, Sep 26 2019 *)
%o (PARI) vector(31, n, f=fibonacci; 2^(n+2) - f(n+4) - f(n+2)) \\ _G. C. Greubel_, Sep 26 2019
%o (Magma) [2^(n+3) - Lucas(n+4): n in [0..30]]; // _G. C. Greubel_, Sep 26 2019
%o (Sage) [2^(n+3) - lucas_number2(n+4,1,-1) for n in (0..30)] # _G. C. Greubel_, Sep 26 2019
%o (GAP) List([0..30], n-> 2^(n+3) - Lucas(1,-1,n+4)[2]); # _G. C. Greubel_, Sep 26 2019
%Y Cf. A000032, A000045, A027960.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_
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