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%I #16 Oct 11 2022 00:52:14
%S 1,3,19,63,307,1095,4843,18111,76483,294327,1213147,4747119,19308979,
%T 76282599,308006731,1223430687,4919576995,19600876311,78636062395,
%U 313847102415,1257480899731,5023648225863,20113423216939,80397210315903,321758305696387,1286524863041655
%N Expansion of 1/((1-2*x)*(1+3*x)*(1-4*x)).
%H Colin Barker, <a href="/A249994/b249994.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 (3,10,-24).
%F G.f.: 1/((1-2*x)*(1+3*x)*(1-4*x)).
%F a(n) = (5*2^(2*n+3) - 7*2^(n+1) + (-1)^n*3^(n+2))/35. - _Colin Barker_, Dec 29 2014
%F a(n) = 3*a(n-1) + 10*a(n-2) - 24*a(n-3). - _Colin Barker_, Dec 29 2014
%F E.g.f.: (1/35)*(9*exp(-3*x) - 14*exp(2*x) + 40*exp(4*x)). - _G. C. Greubel_, Oct 10 2022
%t LinearRecurrence[{3,10,-24}, {1,3,19}, 41] (* _G. C. Greubel_, Oct 10 2022 *)
%o (PARI) Vec(1/((2*x-1)*(3*x+1)*(4*x-1)) + O(x^100)) \\ _Colin Barker_, Dec 29 2014
%o (Magma) [(5*2^(2*n+3) -7*2^(n+1) +(-1)^n*3^(n+2))/35: n in [0..40]]; // _G. C. Greubel_, Oct 10 2022
%o (SageMath) [(5*2^(2*n+3) -7*2^(n+1) +(-1)^n*3^(n+2))/35 for n in range(41)] # _G. C. Greubel_, Oct 10 2022
%Y Cf. A016269 for the expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)).
%Y Cf. A249992, A249993, A249995, A249996.
%K nonn,easy
%O 0,2
%A _Alex Ratushnyak_, Dec 28 2014
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