0,2

Susceptibility series H_1 for 2-dimensional Ising model (divided by 2).

Also the Engel expansion of exp^(1/4); cf. A006784 for the Engel expansion definition - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 03 2002

Number of squares in an n X n board with all non-perimeter squares removed. - Jon Perry (perry(AT)globalnet.co.uk), Jul 27 2003

Number of 2 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00,0), (00;1) and (10;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 and j1<j2 and these elements are in same relative order as those in the triple (x,y,z). - Sergey Kitaev (kitaev(AT)ms.uky.edu), Nov 11 2004

Central terms of the triangle in A118013. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 10 2006

Coordination sequence for 2-dimensional cyclotomic lattice Z[zeta_4].

D. Hansel et al., Analytical properties of the anisotropic cubic Ising model, J. Stat. Phys., 48 (1987), 69-80.

M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136.

T. D. Noe, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

A. J. Guttmann, Indicators of solvability for lattice models, Discrete Math., 217 (2000), 167-189.

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, University of Kentucky Research Reports (2004).

Binomial transform is A000337. - Paul Barry (pbarry(AT)wit.ie), Jul 21 2003

Euler transform of length 2 sequence [ 4, -2]. - Michael Somos Apr 16 2007

G.f.: ((1+x)/ (1-x))^2. E.g.f.: 1 +4*x*exp(x). - Michael Somos Apr 16 2007

a(-n)= -a(n) unless n=0. - Michael Somos Apr 16 2007

Row sums of triangle A130323: (1; 3,1; 5,2,1; 7,3,1,1;...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 24 2007

Row sums of triangle A131032: (1; 3,1; 5,2,1; 7,2,2,1;...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 10 2007

G.f.: exp(4*atanh(x)) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 20 2009]

(PARI) {a(n)= 4*n+!n} /* Michael Somos Apr 16 2007 */

Cf. A054275, A054410, A054389, A054764.

Convolution square of A040000.

Cf. A130323.

Cf. A131032.

Sequence in context: A161352 A008586 A059558 this_sequence A085127 A059532 A034045

Adjacent sequences: A008571 A008572 A008573 this_sequence A008575 A008576 A008577

nonn,nice,easy

N. J. A. Sloane (njas(AT)research.att.com).