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A110614 a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15. 2

%I

%S 1,5,15,57,215,841,3319,13193,52599,210057,839543,3356809,13424503,

%T 53692553,214759287,859015305,3436017527,13743982729,54975756151,

%U 219902675081,879610001271,3518438606985,14073751631735,56295000934537,225179992553335,900719947843721

%N a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.

%C See comment for A110613.

%H Colin Barker, <a href="/A110614/b110614.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 (5,-2,-8).

%F G.f.: (1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)).

%F a(n) + a(n+1) = A063376(n+1).

%F a(n) = (-7*(-1)^n + 5*2^(1+n) + 3*4^(1+n)) / 15. - _Colin Barker_, Feb 05 2017

%p seriestolist(series((1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2ibasejsumseq[(.5'i - .5'k - .5i' + .5k' - .5'ij' - .5'ji' - .5'jk' - .5'kj')('i + j' + 'ij' + 'ji')] Sumtype is set to: sum[Y[15]] = sum[ * ] (disregarding signs)

%t LinearRecurrence[{5,-2,-8},{1,5,15},30] (* _Harvey P. Dale_, Dec 28 2013 *)

%o (PARI) Vec((1-8*x^2)/((4*x-1)*(2*x-1)*(x+1)) + O(x^30)) \\ _Colin Barker_, Feb 05 2017

%Y Cf. A110613, A063376.

%K easy,nonn

%O 0,2

%A _Creighton Dement_, Jul 31 2005

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Last modified October 20 02:18 EDT 2019. Contains 328244 sequences. (Running on oeis4.)