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%I #13 Sep 08 2022 08:44:49
%S 0,0,0,4,7,23,42,106,200,456,879,1903,3718,7814,15396,31780,62951,
%T 128487,255378,517522,1030864,2079440,4147935,8342239,16655822,
%U 33433038,66791052,133899916,267603415,536038871,1071563514,2145305338
%N a(n) is the sum of the non-Fibonacci numbers in row n of array T given by A027935, computed as T(n,m) + T(n,m+1) + ... + T(n,n-1), where m = floor((n+2)/2).
%H G. C. Greubel, <a href="/A027946/b027946.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-9,5,3,-2).
%F G.f.: x^3*(4 - 5*x - 2*x^2 + 2*x^3)/((1-x)*(1-2*x)*(1+x-x^2)*(1-x-x^2)).
%F From _G. C. Greubel_, Sep 28 2019: (Start)
%F a(n) = (2^(n+1) - 2 - Fibonacci(n+3) - (-1)^n*Fibonacci(n))/2, n > 0.
%F a(2*n) = 4^n - 1 - Fibonacci(2*n+2), n > 0.
%F a(2*n+1) = 2^(2*n+1) - 1 - Fibonacci(2*n+2). (End)
%p with(combinat); seq(`if`(n=0,0, (2^(n+1)-2-fibonacci(n+3) -(-1)^n* fibonacci(n))/2), n=0..40); # _G. C. Greubel_, Sep 28 2019
%t Table[If[n==0,0,(2^(n+1) -2 -Fibonacci[n+3] -(-1)^n*Fibonacci[n])/2], {n, 0, 40}] (* _G. C. Greubel_, Sep 28 2019 *)
%o (PARI) concat([0], vector(40, n, (2^(n+1)-2-fibonacci(n+3) -(-1)^n* fibonacci(n))/2)) \\ _G. C. Greubel_, Sep 28 2019
%o (Magma) [0] cat [(2^(n+1)-2-Fibonacci(n+3) -(-1)^n*Fibonacci(n))/2: n in [1..40]]; // _G. C. Greubel_, Sep 28 2019
%o (Sage) [0]+[(2^(n+1)-2-fibonacci(n+3) -(-1)^n*fibonacci(n))/2 for n in (1..40)] # _G. C. Greubel_, Sep 28 2019
%o (GAP) Concatenation([0], List([1..40], n-> (2^(n+1)-2-Fibonacci(n+3) -(-1)^n*Fibonacci(n))/2)); # _G. C. Greubel_, Sep 28 2019
%Y Cf. A000045, A027935.
%K nonn
%O 0,4
%A _Clark Kimberling_
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