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%I #17 Jul 22 2022 01:27:35
%S 1,7,32,122,423,1389,4414,13744,42245,128771,390396,1179366,3554467,
%T 10696153,32153978,96592988,290041089,870647535,2612991160,7841070610,
%U 23527406111,70590606917,211788597942,635399348232,1906265153533,5718929678299,17157057470324,51471709281854
%N Expansion of 1/((1-x)^2*(1-2*x)*(1-3*x)).
%H G. C. Greubel, <a href="/A249999/b249999.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,17,-6).
%F G.f.: 1/((1-x)^2 * (1-2*x) * (1-3*x)).
%F a(n) = 9/4 - 2^(n+3) + n/2 + 3^(n+3)/4. - _R. J. Mathar_, Jan 09 2015
%F E.g.f.: (1/4)*((9 + 2*x) - 32*exp(x) + 27*exp(2*x))*exp(x). - _G. C. Greubel_, Jul 21 2022
%t LinearRecurrence[{7,-17,17,-6}, {1,7,32,122}, 50] (* _G. C. Greubel_, Jul 21 2022 *)
%o (Magma) [(2*n +9 -2^(n+5) +3^(n+3))/4: n in [0..50]]; // _G. C. Greubel_, Jul 21 2022
%o (SageMath) [(2*n+9 -2^(n+5) +3^(n+3))/4 for n in (0..50)] # _G. C. Greubel_, Jul 21 2022
%Y Cf. A000392 (first differences), A094705, A243869, A249997.
%K nonn,easy
%O 0,2
%A _Alex Ratushnyak_, Dec 28 2014
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