%I A033537
%S A033537 0,7,18,33,52,75,102,133,168,207,250,297,348,403,462,525,
%T A033537 592,663,738,817,900,987,1078,1173,1272,1375,1482,1593,
%U A033537 1708,1827,1950,2077,2208,2343,2482,2625,2772,2923,3078
%N A033537 n(2n+5).
%C A033537 Permutations avoiding 12-3 that contain the pattern 32-1 exactly once.
%C A033537 a(n) = A014107(n) + 8*n^2; A100035(a(n)) = 3 for n>1. - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Oct 31 2004
%C A033537 If Y is a 3-subset of an (2n+1)-set X then, for n>=1, a(n-1) is the number 
               of (2n-1)-subsets of X having at least two elements in common with 
               Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 16 2007
%H A033537 T. Mansour, <a href="http://arXiv.org/abs/math.CO/0202219">Restricted 
               permutations by patterns of type 2-1</a>.
%F A033537 a(n)=4*n+a(n-1)-1 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 08 2009]
%e A033537 For n=2, a(2)=4*2+0-1=7; n=3, a(3)=4*3+7-1=18; n=4, a(4)=4*4+18-1=33 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
%t A033537 s=0;lst={s};Do[s+=n++ +7;AppendTo[lst, s], {n, 0, 7!, 4}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
%t A033537 s = 0; lst = {s}; Do[s += 2*n + 1; AppendTo[lst, s], {n, 3, 80, 2}]; 
               lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 15 2009]
%Y A033537 Cf. A100036, A100037, A100038, A100039.
%Y A033537 Sequence in context: A103572 A049532 A156619 this_sequence A000566 A133673 
               A023166
%Y A033537 Adjacent sequences: A033534 A033535 A033536 this_sequence A033538 A033539 
               A033540
%K A033537 nonn,new
%O A033537 0,2
%A A033537 N. J. A. Sloane (njas(AT)research.att.com).