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A110528 a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37. 3

%I

%S 1,10,37,162,681,2890,12237,51842,219601,930250,3940597,16692642,

%T 70711161,299537290,1268860317,5374978562,22768774561,96450076810,

%U 408569081797,1730726404002,7331474697801,31056625195210

%N a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37.

%C Compare with A110526, A110527.

%H G. C. Greubel, <a href="/A110528/b110528.txt">Table of n, a(n) for n = 0..1000</a>

%H Robert Munafo, <a href="http://www.mrob.com/pub/seq/floretion.html">Sequences Related to Floretions</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,5,1).

%F G.f.: -(1 + 7*x + 2*x^2)/((1 + x)*(x^2 + 4*x - 1)).

%F a(n) = (2 - sqrt(5))^n - (-1)^n + (2 + sqrt(5))^n + (1/2)*(2 + sqrt(5))^n*sqrt(5) - (1/2)*(2 - sqrt(5))^n*sqrt(5), with n >= 0. - _Paolo P. Lava_, Oct 02 2008

%F a(n) = Lucas(3*(n + 1))/2 - (-1)^(n). - _Ehren Metcalfe_, Nov 18 2017

%p seriestolist(series(-(1+7*x+2*x^2)/((1+x)*(x^2+4*x-1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')]

%t LinearRecurrence[{3,5,1},{1,10,37},30] (* _Harvey P. Dale_, Apr 21 2016 *)

%o (PARI) x='x+O('x^50); Vec(-(1+7*x+2*x^2)/((1+x)*(x^2+4*x-1))) \\ _G. C. Greubel_, Aug 30 2017

%Y Cf. A110526, A110527.

%K easy,nonn

%O 0,2

%A _Creighton Dement_, Jul 24 2005

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Last modified November 24 07:49 EST 2020. Contains 338607 sequences. (Running on oeis4.)