Search: id:A017569
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%I A017569
%S A017569 4,16,28,40,52,64,76,88,100,112,124,136,148,160,172,184,
%T A017569 196,208,220,232,244,256,268,280,292,304,316,328,340,352,
%U A017569 364,376,388,400,412,424,436,448,460,472,484,496,508,520
%N A017569 12n+4.
%C A017569 Apart from initial term(s), dimension of the space of weight 2n cusp 
               forms for Gamma_0( 46 ).
%C A017569 Number of 6 X n 0-1 matrices avoiding simultaneously the right angled 
               numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;
               1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple 
               (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements 
               are in the same relative order as those in the triple (x,y,z). In 
               general, the number of m x n 0-1 matrices in question is given by 
               2^m+2m(n-1). Cf. m=2: A008574; m=3: A016933; m=4: A022144; m=5: A017293; 
               . - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 13 2004
%C A017569 Except for 4, exponents e such that x^e-x^2+1 is reducible.
%C A017569 If Y and Z are 2-blocks of a (3n+1)-set X then a(n-1) is the number of 
               3-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), 
               Oct 28 2007
%H A017569 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A017569 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A017569 William A. Stein, <a href="http://modular.fas.harvard.edu/Tables/dimskg0n.gp">
               Dimensions of the spaces S_k(Gamma_0(N))</a>
%H A017569 William A. Stein, <a href="http://modular.fas.harvard.edu/Tables/">The 
               modular forms database</a>
%H A017569 S. Kitaev, <a href="http://www.integers-ejcnt.org/vol4.html">On multi-avoidance 
               of right angled numbered polyomino patterns</a>, Integers: Electronic 
               Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
%o A017569 (Other) sage: [i+4 for i in range(525) if gcd(i,12) == 12] # [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), May 21 2009]
%Y A017569 Sequence in context: A046366 A097374 A046361 this_sequence A161335 A121054 
               A160410
%Y A017569 Adjacent sequences: A017566 A017567 A017568 this_sequence A017570 A017571 
               A017572
%K A017569 nonn,easy
%O A017569 0,1
%A A017569 N. J. A. Sloane (njas(AT)research.att.com).

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