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%I #12 Nov 02 2022 07:36:56
%S 0,1,4,10,21,38,62,95,138,192,259,340,436,549,680,830,1001,1194,1410,
%T 1651,1918,2212,2535,2888,3272,3689,4140,4626,5149,5710,6310,6951,
%U 7634,8360,9131,9948,10812,11725,12688,13702,14769,15890,17066,18299,19590,20940,22351
%N Partial sums of A071619.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1).
%F O.g.f.: x*(1 + x)*(1 + x^2)/((1 + x + x^2)*(1 - x)^4).
%F a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) for n > 5.
%F a(n) = (A005898(n) - A049347(n))/9.
%F E.g.f.: exp(-x/2)*(3*exp(3*x/2)*(1 + 8*x + 9*x^2 + 2*x^3) - 3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))/27.
%t LinearRecurrence[{3,-3,2,-3,3,-1},{0,1,4,10,21,38},47]
%Y Partial sums of the main diagonal of A143976.
%Y Cf. A042968 (2nd differences), A071619 (1st differences).
%Y Cf. A005898, A049347.
%K nonn,easy
%O 0,3
%A _Stefano Spezia_, Oct 26 2022
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