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%I
%S 1,1,2,4,7,11,16,22,29,37,46,56,67,79,92,106,121,137,154,172,191,211,
%T 232,254,277,301,326,352,379,407,436,466,497,529,562,596,631,667,704,
%U 742,781,821,862,904,947,991,1036,1082,1129,1177,1226,1276,1327,1379
%N 1+(n-2)*(n-1)/2.
%C a(1)=1; then add 0 to the first number, then 1,2,3,4... and so on.
%D Dairyko, Michael; Tyner, Samantha; Pudwell, Lara; Wynn, Casey. Non-contiguous pattern avoidance in binary trees. Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227. - From _N. J. A. Sloane_, Feb 01 2013
%D L. Pudwell, Pattern avoidance in trees (slides from a talk, mentions many sequences), http://faculty.valpo.edu/lpudwell/slides/notredame.pdf, 2012. - From _N. J. A. Sloane_, Jan 03 2013
%H <a href="/index/Rea#recLCC">Index entries for sequences related to linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 1+A000217(n-2) = A000124(n-2), n>1. [From _R. J. Mathar_, Jan 03 2009]
%F a(n) = a(n-1)+n-2 (with a(1)=1). [From Vincenzo Librandi, Nov 26 2010]
%F G.f.: -x*(1-2*x+2*x^2)/(x-1)^3.
%t s=1;lst={1};Do[s+=n;AppendTo[lst,s],{n,0,5!}];lst
%o (Sage) [1+binomial(n,2) for n in xrange(0, 54)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
%o (MAGMA) [ 1+(n-2)*(n-1)/2: n in [1..60] ];
%Y Cf. A000217.
%K nonn,easy
%O 1,3
%A _Vladimir Joseph Stephan Orlovsky_, Dec 15 2008
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