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%I #21 Sep 16 2024 12:01:21
%S 3,7,17,37,87,187,437,937,2187,4687,10937,23437,54687,117187,273437,
%T 585937,1367187,2929687,6835937,14648437,34179687,73242187,170898437,
%U 366210937,854492187,1831054687,4272460937,9155273437,21362304687,45776367187,106811523437
%N Sum_{T(i,j)}, 0<=j<=i, 0<=i<=n, where T is the array in A026386.
%H Colin Barker, <a href="/A026396/b026396.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 (1,5,-5).
%F G.f.: (3+4*x-5*x^2) / ((1-x)*(1-5*x^2)). - _Ralf Stephan_, Apr 30 2004
%F From _Colin Barker_, Nov 25 2016: (Start)
%F a(n) = (7*5^(n/2) - 1)/2 for n even.
%F a(n) = (6*5^((n+1)/2) - 2)/4 for n odd.
%F a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) for n>2. (End)
%F a(n) = (3-(-1)^n-(13+(-1)^n)*5^((1-(-1)^n+2*n)/4))/(2*(-1)^n-6). - _Wesley Ivan Hurt_, Oct 02 2021
%t LinearRecurrence[{1, 5, -5}, {3, 7, 17}, 50] (* _Paolo Xausa_, Sep 16 2024 *)
%o (PARI) Vec((-5*x^2 + 4*x + 3)/(5*x^3 - 5*x^2 - x + 1) + O(x^40)) \\ _Colin Barker_, Nov 25 2016
%Y Cf. A026386.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_