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A152947 1+(n-2)*(n-1)/2. 7

%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 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, Non-contiguous 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/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. - _R. J. Mathar_, Jan 03 2009

%F a(n) = a(n-1) + n - 2 (with a(1) = 1). - _Vincenzo Librandi_, Nov 26 2010

%F G.f.: -x*(1-2*x+2*x^2)/(x-1)^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+(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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Last modified December 19 11:29 EST 2014. Contains 252211 sequences.