1,2

Number of ways of covering 2n x 2n lattice with 2n^2 dominoes with exactly 2 horizontal dominoes.

Equals binomial transform of [1, 8, 13, 6, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 14 2008

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)

Sequence of the absolute values of the z^1 coefficients of the polynomials in the GF3 denominators of A156927. See A157704 for background information.

(End)

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 194.

L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 2.

M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Physical Review, 124 (1961), 1664-1672.

P.W. Kasteleyn, The statistics of dimers on a lattice, Physica, 27(1961), 1209-1225.

T. D. Noe, Table of n, a(n) for n=1..1000

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Index entries for sequences related to dominoes

a(n) = odd numbers * triangular numbers - Xavier Acloque Oct 27 2003

a(n)= n*(n+1)*(2*n-1)/2, n>=1. G.f.: x*(1+5*x)/(1-x)^4.

(2*n+1)*binomial(2+n,2). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 12 2006

a(n) = A000578(n) + A000217(n-1) - Kieren MacMillan (kieren(AT)alumni.rice.edu), Mar 19 2007

a(2) = 9 since there are 9 ways to cover a 4 X 4 lattice with 8 dominoes, 2 of which is horizontal and the other 6 are vertical.

A002414 := n-> 1/2*n*(n+1)*(2*n-1);

A002414:=(1+5*z)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)

nmax:=38; for n from 0 to nmax do fz(n):=product((1-(k+1)*z)^(1+3*k), k=0..n); c(n):= abs(coeff(fz(n), z, 1)); end do: a:=n-> c(n): seq(a(n), n=0..nmax);

(End)

a:=n->sum (j*(n+1)+n*(j-1), j=0..n): seq(a(n), n=1..40); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 18 2009]

f[n_]:=6*n+1; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]

Table[Sum[(n^2 - i), {i, 0, n}], {n, 1, 40}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 11 2009]

Cf. A004003.

Cf. A002411.

Cf. A093563 (( 6, 1) Pascal, column m=3). A000567 (differences).

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Mar 07 2009: (Start)

Cf. A156927, A157704.

(End)

Sequence in context: A005919 A084370 A000439 this_sequence A000440 A161684 A054310

Adjacent sequences: A002411 A002412 A002413 this_sequence A002415 A002416 A002417

nonn,easy,nice

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

Additional comments from Yong Kong (ykong(AT)curagen.com), May 06 2000

More terms from Larry Reeves (larryr(AT)acm.org), May 09 2000