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%I #26 Sep 08 2022 08:45:12
%S 1,3,9,24,57,122,239,435,745,1213,1893,2850,4161,5916,8219,11189,
%T 14961,19687,25537,32700,41385,51822,64263,78983,96281,116481,139933,
%U 167014,198129,233712,274227,320169,372065,430475,495993,569248,650905,741666,842271
%N Expansion of (1-3*x+6*x^2-5*x^3+3*x^4-x^5)/(1-x)^6.
%H A. Burstein and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0112281">Words restricted by 3-letter ...</a>, arXiv:math/0112281 [math.CO], 2001.
%H A. Burstein and T. Mansour, <a href="http://dx.doi.org/10.1007/s000260300000">Words restricted by 3-letter ...</a>, Annals. Combin., 7 (2003), 1-14; see Example 3.5.
%H S. Kitaev, J. Remmel, <a href="http://arxiv.org/abs/1503.00914">p-Ascent Sequences</a>, arXiv preprint arXiv:1503.00914 [math.CO], 2015.
%H Sergey Kitaev, J. B. Remmel, <a href="https://pure.strath.ac.uk/portal/files/46917816/Kitaev_Remmel_JC2016_a_note_on_p_ascent_sequences.pdf">A note on p-Ascent Sequences</a>, Preprint, 2016.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(0)=1, a(1)=3, a(2)=9, a(3)=24, a(4)=57, a(5)=122, a(n)=6*a(n-1)- 15*a(n-2)+ 20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). -_Harvey P. Dale_, Jul 18 2012
%F a(n) = 13*n/15+1+n^3/8+11*n^2/12+n^5/120+n^4/12. - _R. J. Mathar_, Sep 27 2014
%t CoefficientList[Series[(1-3x+6x^2-5x^3+3x^4-x^5)/(1-x)^6,{x,0,40}],x] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,3,9,24,57,122},40] (* _Harvey P. Dale_, Jul 18 2012 *)
%o (Magma) I:=[1,3,9,24,57,122]; [n le 6 select I[n] else 6*Self(n-1)- 15*Self(n-2)+ 20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..50]]; // _Vincenzo Librandi_, Nov 19 2015
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jan 18 2004
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