A091003 - OEIS

%I #15 Sep 08 2022 08:45:12

%S 1,-1,4,-10,34,-94,298,-862,2650,-7822,23722,-70654,212986,-636910,

%T 1914826,-5736286,17225242,-51642958,154994410,-464852158,1394818618,

%U -4183931566,12552843274,-37656432670,112973492314,-338912088334,1016753042218

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

%C Inverse binomial transform of A091000.

%H G. C. Greubel, <a href="/A091003/b091003.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,6).

%F 2^n = A091003(n) + 3*A091004(n) + 6*A091005(n).

%F a(n) = (2^n + 4*(-3)^n + 5*0^n)/10.

%F E.g.f.: (exp(2*x) + 4*exp(-3*x) + 5)/10. - _G. C. Greubel_, Feb 01 2019

%t CoefficientList[Series[(1-3x^2)/((1-2x)(1+3x)),{x,0,30}],x] (* _Harvey P. Dale_, Dec 23 2014 *)

%t Join[{1}, LinearRecurrence[{-1,6}, {-1,4}, 30]] (* _G. C. Greubel_, Feb 01 2019 *)

%o (PARI) vector(30, n, n--; (2^n + 4*(-3)^n + 5*0^n)/10) \\ _G. C. Greubel_, Feb 01 2019

%o (Magma) [1] cat [(2^n + 4*(-3)^n)/10: n in [1..30]]; // _G. C. Greubel_, Feb 01 2019

%o (Sage) [1] + [(2^n + 4*(-3)^n)/10 for n in (1..30)] # _G. C. Greubel_, Feb 01 2019

%o (GAP) Concatenation([1], List([1..30], n -> (2^n + 4*(-3)^n)/10)) # _G. C. Greubel_, Feb 01 2019

%K easy,sign

%O 0,3

%A _Paul Barry_, Dec 13 2003