%I A005573 M3943
%S A005573 1,5,26,139,758,4194,23460,132339,751526,4290838,24607628,141648830,
%T A005573 817952188,4736107172,27487711752,159864676803,931448227590,
%U A005573 5435879858958,31769632683132,185918669183370,1089302293140564
%N A005573 Number of walks on cubic lattice (starting from origin and not going 
               below xy plane).
%C A005573 Binomial transform of A026378, second binomial transform of A001700 . 
               - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 28 2007
%C A005573 The Hankel transform of [1,1,5,26,139,758,...] is [1,4,15,56,209,...](see 
               A001353). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 13 2007
%D A005573 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005573 E. Deutsch et al., Problem 10795, Amer. Math. Monthly, 108 (Dec. 2001), 
               980.
%H A005573 R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">J. Integer Seqs., Vol. 3 (2000), #00.1.6</
               a>
%F A005573 sum((-1)^i*6^(n-i)*binomial(n, i)*binomial(2*i, i)/(i+1), i=0..n); g.f. 
               A(x) satisfies x(1-6x)A^2+(1-6x)A-1=0 - from Emeric Deutsch (deutsch(AT)duke.poly.edu); 
               corrected by Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Jan 
               09 2003
%F A005573 a(n) = 6a(n-1)-A005572(n-1) = sum{j = 0, ..., n}[4^(n-j)*C(n, [n/2])*C(n, 
               j)] - Henry Bottomley (se16(AT)btinternet.com), Aug 23 2001
%F A005573 a(n) = sum_{k=0..n} binomial(n, k)*binomial(2*k+1, k)*2^(n-k).
%F A005573 a(n) = sum_{k=0..n} (-1)^k*binomial(n, k)*Catalan(k)*6^(n-k).
%F A005573 (n+1)*a(n) = (8*n+2)*a(n-1)-(12*n-12)*a(n-2). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jul 16 2004
%F A005573 a(n) = Sum_{k, 0<=k<=n} A052179(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jan 28 2007
%F A005573 Contribution from Paul Barry (pbarry(AT)wit.ie), Apr 21 2009: (Start)
%F A005573 G.f.: (sqrt((1-2x)/(1-6x))-1)/(2x);
%F A005573 G.f.: 1/(1-5x-x^2/(1-4x-x^2/(1-4x-x^2/(1-4x-x^2/(1-... (continued fraction). 
               (End)
%Y A005573 Sequence in context: A049607 A035029 A081569 this_sequence A081911 A081187 
               A104498
%Y A005573 Adjacent sequences: A005570 A005571 A005572 this_sequence A005574 A005575 
               A005576
%K A005573 nonn,easy,nice
%O A005573 0,2
%A A005573 N. J. A. Sloane (njas(AT)research.att.com).
%E A005573 More terms from Henry Bottomley (se16(AT)btinternet.com), Aug 23 2001