Search: id:A024206
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%I A024206
%S A024206 0,1,3,5,8,11,15,19,24,29,35,41,48,55,63,71,80,89,99,109,120,131,143,
%T A024206 155,168,181,195,209,224,239,255,271,288,305,323,341,360,379,399,419,
%U A024206 440,461,483,505,528,551,575,599,624,649,675,701,728,755,783,811,840
%N A024206 Expansion of x^2*(1+x-x^2)/((1-x^2)*(1-x)^2).
%C A024206 a(n+1) is the number of 2 X n binary matrices with no zero rows or columns, 
               up to row and column permutation.
%C A024206 [ (4th elementary symmetric function of S(n))/(3rd elementary symmetric 
               function of S(n)) ], where S(n) = {first n+3 odd positive integers}.
%C A024206 Let M_n denotes the n X n matrix m(i,j) = 1 if i =j; m(i,j) = 1 if (i+j) 
               is odd; m(i,j) = 0 if i+j is even, then a(n) = -det M_(n+1) - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Jun 19 2002
%C A024206 a(n) = A002620(n+1)-1.
%C A024206 a(n) = number of squares with corners on an n X n grid, distinct up to 
               translation. See also A002415, A108279.
%C A024206 Number of solutions to x+y >= n-1 in integers x,y with 1 <= x <= y <= 
               n-1. - Franz Vrabec (franz.vrabec(AT)aon.at), Feb 22 2008
%H A024206 Thomas Wieder, The number of certain k-combinations of an n-set, <a href="http:/
               /www.math.nthu.edu.tw/~amen/">Applied Mathematics Electronic Notes</
               a>, vol. 8 (2008).
%F A024206 a(n+1) = A002620(n) + n, n>=0 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Feb 27 2004
%F A024206 a(0)=0, a(n) = floor(a(n-1)+sqrt(a(n-1))+1) for n > 0 - Gerald McGarvey 
               (Gerald.Mcgarvey(AT)comcast.net), Jul 30 2004
%F A024206 Starting (1, 3, 5, 8, 11,...), = row sums of triangle A135841. - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Dec 01 2007
%F A024206 a(n) = floor((n+1)^2/4)-1. - Franz Vrabec (franz.vrabec(AT)aon.at), Feb 
               22 2008
%F A024206 a(n)=A005744(n-1)-A005744(n-2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 04 2008]
%F A024206 a(n)=a(n-1) + [side length of the least square > a(n-1) ] , that is a(n)= 
               a(n-1)+ ceiling(sqrt(a(n-1)+1)). [From Ctibor O. ZIZKA (c.zizka(AT)email.cz), 
               Oct 06 2009]
%e A024206 There are 5 2 X 3 binary matrices with no zero rows or columns up to 
               row and column permutation:
%e A024206 [1 0 0] [1 0 0] [1 1 0] [1 1 0] [1 1 1]
%e A024206 [0 1 1] [1 1 1] [0 1 1] [1 1 1] [1 1 1].
%Y A024206 a(n+1)=A002623(n)-A002623(n-1)-1.
%Y A024206 Cf. A135841.
%Y A024206 Sequence in context: A145197 A024169 A078126 this_sequence A159325 A049706 
               A080415
%Y A024206 Adjacent sequences: A024203 A024204 A024205 this_sequence A024207 A024208 
               A024209
%K A024206 nonn,easy,nice
%O A024206 1,3
%A A024206 Clark Kimberling (ck6(AT)evansville.edu)
%E A024206 Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 
               02 2000

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