%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+(n2)*(n1)/2.
%C The sequence is the sum of upward sloping terms in an infinite lower triangle with 1's in the leftmost column and the odd integers in all other columns.  _Gary W. Adamson_, Jan 29 2014
%D Michael Dairyko, Samantha Tyner, Lara Pudwell, Casey Wynn, Noncontiguous pattern avoidance in binary trees, Electron. J. Combin. 19 (2012), no. 3, Paper 22, 21 pp. MR2967227.
%H H. Cheballah, S. Giraudo, R. Maurice, <a href="http://arxiv.org/abs/1306.6605">Combinatorial Hopf algebra structure on packed square matrices</a>, arXiv preprint arXiv:1306.6605, 2013
%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/slides/notredame.pdf">Pattern avoidance in trees</a> (slides from a talk, mentions many sequences), http://faculty.valpo.edu/lpudwell/slides/notredame.pdf, 2012.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,1).
%F a(n) = 1 + A000217(n2) = A000124(n2), n > 1.  _R. J. Mathar_, Jan 03 2009
%F a(n) = a(n1) + n  2 (with a(1) = 1).  _Vincenzo Librandi_, Nov 26 2010
%F G.f.: x*(12*x+2*x^2)/(x1)^3.
%t s = 1; A152947 = {1}; Do[s += n; AppendTo[A152947, s], {n, 0, 5!}]; A152947 (* Orlowski *)
%t Table[1 + (n^2  3n + 2)/2, {n, 50}] (* _Alonso del Arte_, Jan 30 2014 *)
%o (Sage) [1+binomial(n,2) for n in xrange(0, 54)] # _Zerinvary Lajos_, Mar 12 2009
%o (MAGMA) [ 1+(n2)*(n1)/2: n in [1..60] ];
%Y Cf. A000217.
%K nonn,easy
%O 1,3
%A _Vladimir Joseph Stephan Orlovsky_, Dec 15 2008
