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A027958 a(n) = T(n,m) + T(n,m+1) + ... + T(n,n), where m = floor((n+2)/2), T given by A027948.

%I A027958 #15 Sep 08 2022 08:44:49
%S A027958 1,1,4,5,20,32,95,169,424,793,1816,3488,7583,14789,31172,61357,126892,
%T A027958 251200,513343,1019921,2068496,4119281,8313584,16580800,33358015,
%U A027958 66594637,133703500,267089189,535524644,1070217248,2143959071
%N A027958 a(n) = T(n,m) + T(n,m+1) + ... + T(n,n), where m = floor((n+2)/2), T given by A027948.
%C A027958 a(n) is the sum of the terms of the 2nd half of the n-th row of the A027948 triangle. - _Michel Marcus_, Oct 01 2019
%H A027958 G. C. Greubel, <a href="/A027958/b027958.txt">Table of n, a(n) for n = 1..1000</a>
%H A027958 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-8,-4,8,1,-2).
%F A027958 G.f.: x*(1 -x -2*x^2 + x^3 +6*x^4 -2*x^6)/((1-2*x)*(1-x^2)(1+x-x^2)*(1-x-x^2)).
%F A027958 a(n) = (3 +(-1)^n +2^(n+1) -(-1)^n*Fibonacci(n+1) -Fibonacci(n+4))/2. - _G. C. Greubel_, Sep 30 2019
%p A027958 f:= combinat[fibonacci]: seq((3 +(-1)^n +2^(n+1) -(-1)^n*f(n+1) -f(n+4))/2, n=1..40); # _G. C. Greubel_, Sep 30 2019
%t A027958 Table[(3 +(-1)^n +2^(n+1) -(-1)^n*Fibonacci[n+1] -Fibonacci[n+4])/2, {n,40}] (* _G. C. Greubel_, Sep 30 2019 *)
%o A027958 (PARI) vector(40, n, f=fibonacci; (3 +(-1)^n +2^(n+1) -(-1)^n*f(n+1) -f(n+4))/2 ) \\ _G. C. Greubel_, Sep 30 2019
%o A027958 (Magma) F:=Fibonacci; [(3 +(-1)^n +2^(n+1) -(-1)^n*F(n+1) -F(n+4))/2: n in [1..40]]; // _G. C. Greubel_, Sep 30 2019
%o A027958 (Sage) f=fibonacci; [(3 +(-1)^n +2^(n+1) -(-1)^n*f(n+1) -f(n+4))/2 for n in (1..40)] # _G. C. Greubel_, Sep 30 2019
%o A027958 (GAP) F:=Fibonacci;; List([1..40], n-> (3 +(-1)^n +2^(n+1) -(-1)^n*F(n+1) -F(n+4))/2); # _G. C. Greubel_, Sep 30 2019
%Y A027958 Cf. A000045, A027948.
%K A027958 nonn
%O A027958 1,3
%A A027958 _Clark Kimberling_