%I A002895 M3626 N1473
%S A002895 1,4,28,256,2716,31504,387136,4951552,65218204,878536624,12046924528,
%T A002895 167595457792,2359613230144,33557651538688,481365424895488,
%U A002895 6956365106016256,101181938814289564,1480129751586116848
%N A002895 Number of 2n-step polygons on diamond lattice.
%C A002895 a(n) is the (2n)th moment of the distance from the origin of a 4-step 
               random walk in the plane - Peter M.W. Gill (peter.gill(AT)nott.ac.uk), 
               Mar 03 2004
%D A002895 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002895 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002895 David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, 
               Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.
%D A002895 C. Domb, On the theory of cooperative phenomena in crystals, Advances 
               in Phys., 9 (1960), 149-361.
%D A002895 J. A. Hendrickson, Jr., On the enumeration of rectangular (0,1)-matrices, 
               Journal of Statistical Computation and Simulation, 51 (1995), 291-313.
%H A002895 L. B. Richmond, J. Shallit, <a href="http://arxiv.org/abs/0807.5028">
               Counting Abelian Squares</a>, arXiv:0807.5028 [Math.CO]. [From R. 
               J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2008]
%F A002895 Sum_{k=0..n} binomial(n, k)^2 binomial(2n-2k, n-k) binomial(2k, k).
%F A002895 n^3*a(n) = 2*(2*n-1)*(5*n^2-5*n+2)*a(n-1)-64*(n-1)^3*a(n-2). - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Jul 16 2004
%F A002895 Sum_{n>=0} a(n)*x^n/n!^2 = BesselI(0, 2*sqrt(x))^4. - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Aug 01 2006
%Y A002895 Cf. A002893.
%Y A002895 Sequence in context: A112113 A103211 A064340 this_sequence A141004 A152410 
               A138272
%Y A002895 Adjacent sequences: A002892 A002893 A002894 this_sequence A002896 A002897 
               A002898
%K A002895 nonn,easy,nice,walk
%O A002895 0,2
%A A002895 N. J. A. Sloane (njas(AT)research.att.com).
%E A002895 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 11 2003