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 A110683 Expansion of (7*x^2+3*x-1)*(2*x^2+2*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)). 4

%I #16 Sep 06 2017 14:29:03

%S 1,-7,21,-79,279,-997,3561,-12781,45951,-165355,595143,-2142025,

%T 7709073,-27743437,99840687,-359294443,1292981391,-4653011185,

%U 16744655841,-60258539413,216850840215,-780375582475,2808317778903,-10106221816681,36369003278769

%N Expansion of (7*x^2+3*x-1)*(2*x^2+2*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)).

%H G. C. Greubel, <a href="/A110683/b110683.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-6, -10, -3, 8, 6, 6).

%F a(0)=1, a(1)=-7, a(2)=21, a(3)=-79, a(4)=279, a(5)=-997, a(n)= -6*a(n-1)- 10*a(n-2)-3*a(n-3)+8*a(n-4)+6*a(n-5)+6*a(n-6). - _Harvey P. Dale_, May 08 2011

%p seriestolist(series((7*x^2+3*x-1)*(2*x^2+2*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: tessum(infty)-2tesforsumseq[ + 'i - .25'j + .25'k - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e], Sumtype is set to: sum[Y[15]] = sum[ * ], Fortype is set to: 1A.

%t LinearRecurrence[{-6,-10,-3,8,6,6},{1,-7,21,-79,279,-997},40] (* or *) CoefficientList[Series[(7x^2+3x-1)(2x^2+2x+1)/((x-1)(3x^2+3x+1)(2x^3+ 2x^2+4x+1)),{x,0,40}],x] (* _Harvey P. Dale_, May 08 2011 *)

%o (PARI) Vec((7*x^2+3*x-1)*(2*x^2+2*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012

%Y Cf. A110684, A110685, A110686.

%K sign,easy

%O 0,2

%A _Creighton Dement_, Aug 02 2005

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Last modified November 29 03:03 EST 2023. Contains 367422 sequences. (Running on oeis4.)