%I A116699
%S A116699 1,2,5,13,30,61,112,190,303,460,671,947,1300,1743,2290,2956,3757,4710,
%T A116699 5833,7145,8666,10417,12420,14698,17275,20176,23427,27055,31088,35555,
%U A116699 40486,45912,51865,58378,65485,73221,81622,90725,100568,111190,122631
%N A116699 Number of permutations of length n which avoid the patterns 123 and 4312.
%C A116699 Also number of permutations of length n which avoid the patterns 123, 
               2314, 4312; or avoid the patterns 321, 1243, 3421, etc.
%H A116699 Lara Pudwell, <a href="http://www.math.rutgers.edu/~lpudwell/webbook/
               bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%F A116699 G.f.: A(x) = {x(2x^3-5x^2+3x-1)}/{(x-1)^5}
%F A116699 a(n) = (n^4 + 2n^3 - 13n^2 + 34n)/24. - Franklin T. Adams-Watters, Sep 
               16 2006
%F A116699 Partial sums of A105163. - Levi R. Self (levi.r.self(AT)gmail.com), Aug 
               04 2007
%F A116699 Binomial transform of [1, 1, 2, 3, 1, 0, 0, 0,...]. - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Oct 23 2007
%o A116699 (PARI) for(n=1,100,print1((n^4 + 2*n^3 - 13*n^2 + 34*n)/24",")) - Herman 
               Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008
%Y A116699 Sequence in context: A045703 A122025 A057873 this_sequence A054127 A018012 
               A065377
%Y A116699 Adjacent sequences: A116696 A116697 A116698 this_sequence A116700 A116701 
               A116702
%K A116699 nonn,easy
%O A116699 1,2
%A A116699 Lara Pudwell (Lara.Pudwell(AT)valpo.edu), Feb 26 2006
%E A116699 Edited by N. J. A. Sloane (njas(AT)research.att.com), Mar 16 2008
%E A116699 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 22 2008