A249996 - OEIS

%I #17 Oct 11 2022 07:39:10

%S 1,-1,15,-5,191,99,2455,3515,33231,74899,474695,1371435,7071871,

%T 23520899,108399735,390617755,1691480111,6378762099,26676785575,

%U 103221406475,423343881951,1661998662499,6742129440215,26686105001595,107591675061391,427824901526099,1718925069371655

%N Expansion of 1/((1+2*x)*(1+3*x)*(1-4*x)).

%H Colin Barker, <a href="/A249996/b249996.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 (-1,14,24).

%F G.f.: 1 / ((1+2*x)*(1+3*x)*(1-4*x)).

%F a(n) = ( 2^(3+2*n) + (3^(3+n)-7*2^(1+n))*(-1)^n )/21. - _Colin Barker_, Dec 29 2014

%F a(n) = -a(n-1) + 14*a(n-2) + 24*a(n-3). - _Colin Barker_, Dec 29 2014

%F E.g.f.: (1/21)*(27*exp(-3*x) - 14*exp(-2*x) + 8*exp(4*x)). - _G. C. Greubel_, Oct 11 2022

%t LinearRecurrence[{-1,14,24}, {1,-1,15}, 41] (* _G. C. Greubel_, Oct 11 2022 *)

%o (PARI) Vec(1/((1+2*x)*(1+3*x)*(1-4*x)) + O(x^50)) \\ _Michel Marcus_, Dec 29 2014

%o (Magma) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21: n in [0..40]]; // _G. C. Greubel_, Oct 11 2022

%o (SageMath) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21 for n in range(41)] # _G. C. Greubel_, Oct 11 2022

%Y Cf. A016269: expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)).

%Y Cf. A249992, A249993, A249994, A249995.

%K sign,easy

%O 0,3

%A _Alex Ratushnyak_, Dec 28 2014