%I #24 Mar 07 2020 01:15:57

%S 1,2,5,12,22,34,48,64,82,102,124,148,174,202,232,264,298,334,372,412,

%T 454,498,544,592,642,694,748,804,862,922,984,1048,1114,1182,1252,1324,

%U 1398,1474,1552,1632,1714,1798,1884,1972,2062,2154,2248,2344,2442,2542

%N Expansion of (1 - x + 2*x^2 + 2*x^3 - x^4 - x^5)/(1-x)^3.

%C Also, number of permutations of length n+1 which avoid the patterns 321, 1342, 2134. - _Lara Pudwell_, Feb 26 2006

%H Colin Barker, <a href="/A048840/b048840.txt">Table of n, a(n) for n = 0..1000</a>

%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.

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

%F For n > 2, a(n) = n^2 + 3n - 6.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 5. - _Colin Barker_, May 03 2019

%t CoefficientList[Series[(1-x+2*x^2+2*x^3-x^4-x^5)/(1-x)^3,{x,0,60}],x] (* or *) Join[{1,2,5},Table[n^2+3*n-6,{n,3,60}]] (* or *) Join[{1,2,5},LinearRecurrence[{3,-3,1},{12,22,34},58]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 31 2012 *)

%o (PARI) Vec((1-x+2*x^2+2*x^3-x^4-x^5)/(1-x)^3 + O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012, corrected by _Colin Barker_, May 03 2019

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_