Search: id:A006958
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%I A006958 M1175
%S A006958 1,2,4,9,20,46,105,242,557,1285,2964,6842,15793,36463,84187,194388,
%T A006958 448847,1036426,2393208,5526198,12760671,29466050,68041019,157115917,
%U A006958 362802072,837759792,1934502740,4467033943,10314998977,23818760154
%N A006958 Number of staircase polyominoes with n cells.
%D A006958 E. A. Bender, Convex n-ominoes, Discrete Math., 8 (1974), 219-226.
%D A006958 D. A. Klarner and R. L. Rivest, Asymptotic bounds for the number of convex 
               n-ominoes, Discrete Math., 8 (1974), 31-40.
%D A006958 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006958 P. Flajolet, <a href="http://algo.inria.fr/flajolet/Publications/publist.html">
               Polya Festoons</a>, INRIA Research Report, No 1507, September 1991. 
               6pp.
%H A006958 D. Gouyou-Beauchamps and P. Leroux, <a href="http://www.arXiv.org/abs/
               math.CO/0403168">Enumeration of symmetry classes of convex polyominoes 
               on the honeycomb lattice</a>.
%H A006958 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               661
%F A006958 G.f.: 1+A(x) = 1/(1-x/(1-x/(1-x^2/(1-x^2/(1-x^3/(1-x^3/(1-...)))))) (continued 
               fraction). - Paul D. Hanna (pauldhanna(AT)juno.com), May 14 2005
%F A006958 The continued fraction given by P. Flajolet, "Polya Festoons", is derived 
               from a q-expansion, C(x, y;q), where C(1, 1;q) = q/(1-2*q-q^3/(1-2*q^2-q^5/
               (1-2*q^3-q^7/(1-2*q^4-q^9/(1-...))))) = q + 2*q^2 + 4*q^3 + 9*q^4 
               + 20*q^5 + 46*q^6 + 105*q^7 +... - Paul D. Hanna (pauldhanna(AT)juno.com), 
               May 14 2005
%e A006958 G.f. may be expressed by the continued fraction: 1/(1-x/(1-x/(1-x^2/(1-x^2/
               (1-x^3/(1-x^3/(1-x^4/(1-...))))))))) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 
               + 20*x^5 + 46*x^6 + 105*x^7 +...
%p A006958 n:=100: C11q:=1-2*q^n-q^(2*n+1): for i from n-1 by -1 to 1 do C11q:=1-2*q^i-q^(2*i+1)/
               C11q od:C11q:=q/C11q:seq(coeff(convert(series(C11q,q,100),polynom),
               q,n),n=1..50); (Pab Ter)
%o A006958 (PARI) {a(n)=local(CF=1+x*O(x^n),m); for(k=0,n\2,m=n\2-k+1;CF=(1-x^((m+1)\2)/
               CF));polcoeff(1/CF,n)} (Hanna)
%Y A006958 Sequence in context: A111099 A000632 A090245 this_sequence A036617 A007902 
               A057417
%Y A006958 Adjacent sequences: A006955 A006956 A006957 this_sequence A006959 A006960 
               A006961
%K A006958 nonn,nice
%O A006958 1,2
%A A006958 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A006958 More terms from Paul D. Hanna (pauldhanna(AT)juno.com), May 14 2005

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