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%I #12 Jul 22 2022 01:27:30
%S 1,2,15,40,221,702,3355,11780,52041,193402,817895,3138720,12953461,
%T 50618102,206059635,813476860,3286192481,13047914802,52482224575,
%U 209057202200,838843897101,3347530323502,13413657088715,53584020970740,214547906035321,857556157684202
%N Expansion of 1/((1-x)*(1+3*x)*(1-4*x)).
%H G. C. Greubel, <a href="/A249997/b249997.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 (2,11,-12).
%F G.f.: 1/((1-x) * (1+3*x) * (1-4*x)).
%F a(n) = (-1)^n*3^(n+2)/28 + 4^(n+2)/21 -1/12. - _R. J. Mathar_, Jan 09 2015
%F E.g.f.: (1/84)*(27*exp(-3*x) - 7*exp(x) + 64*exp(4*x)). - _G. C. Greubel_, Jul 21 2022
%t LinearRecurrence[{2,11,-12}, {1,2,15}, 50] (* _G. C. Greubel_, Jul 21 2022 *)
%o (Magma) [((-1)^n*3^(n+3) +4^(n+3) -7)/84: n in [0..50]]; // _G. C. Greubel_, Jul 21 2022
%o (SageMath) [((-1)^n*3^(n+3) +4^(n+3) -7)/84 for n in (0..50)] # _G. C. Greubel_, Jul 21 2022
%Y Cf. A016208, A099621, A249998, A249999.
%K nonn,easy
%O 0,2
%A _Alex Ratushnyak_, Dec 28 2014