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%I #10 Jan 31 2023 08:29:52
%S 1,6,15,28,46,69,96,127,163,204,249,298,352,411,474,541,613,690,771,
%T 856,946,1041,1140,1243,1351,1464,1581,1702,1828,1959,2094,2233,2377,
%U 2526,2679,2836,2998,3165,3336,3511,3691,3876,4065,4258,4456,4659
%N Partial sums of A301291.
%H Colin Barker, <a href="/A301292/b301292.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,4,-3,1).
%F From _Colin Barker_, Mar 23 2018: (Start)
%F G.f.: (1 + 3*x + x^2 + 3*x^3 + x^4)/((1 - x)^3*(1 + x^2)).
%F a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n > 4.
%F (End)
%F From _Stefano Spezia_, Jan 30 2023: (Start)
%F a(n) = (5 + 9*n*(1 + n) - A087960(n))/4.
%F E.g.f.: (exp(x)*(5 + 18*x + 9*x^2) - cos(x) + sin(x))/4. (End)
%o (PARI) Vec((1 + 3*x + x^2 + 3*x^3 + x^4) / ((1 - x)^3*(1 + x^2)) + O(x^60)) \\ _Colin Barker_, Mar 23 2018
%Y Cf. A087960, A301291.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Mar 23 2018