4,7

Rows are numbers of dominoes with k spots where each half-domino has zero to n spots (in standard domino set: n=6, there are 28 dominoes and row is 1,1,2,2,3,3,4,3,3,2,2,1,1) - Henry Bottomley (se16(AT)btinternet.com), Aug 23 2000

The Gaussian polynomial (or Gaussian binomial) [n,2]_q is an example of a q-binomial coefficient (see the link) and may be defined for n >= 2 by [n,2]_q = ([n]_q * [n-1]_q)/([1]_q * [2]_q), where [n]_q := q^n - 1. The first few values are: [2,2]_q = 1; [3,2]_q = 1 + q + q^2; [4,2]_q = 1 + q + 2q^2 + q^3 + q^4. - Peter Bala (pbala(AT)toucansurf.com), Sep 23 2007

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 242.

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 236.

Eric Weisstein's World of Mathematics, q-Binomial Coefficient.

Index entries for sequences related to dominoes

Let f(r) = Product( (x^i-x^(r+1))/(1-x^i), i = 1..r-2) / x^((r-1)*(r-2)/2); then expanding f(r) in powers of x and taking coefficients gives the successive rows of this triangle (with a different offset).

Expanding (q^n - 1)(q^(n+1) - 1)/((q - 1)(q^2 - 1)) in powers of q and taking coefficients gives the n th row of the triangle. Ordinary generating function: 1/((1-x)(1-qx)(1-q^2x)) = 1 + x(1 + q + q^2) + x^2(1 + q + 2q^2 + q^3 + q^4) + .... - Peter Bala (pbala(AT)toucansurf.com), Sep 23 2007

1; 1,1,1; 1,1,2,1,1; 1,1,2,2,2,1,1; 1,1,2,2,3,2,2,1,1; 1,1,2,2,3,3,3,2,2,1,1; ...

Cf. A047971, A008968, A106822.

Sequence in context: A002635 A108244 A124961 this_sequence A094189 A122771 A112188

Adjacent sequences: A008964 A008965 A008966 this_sequence A008968 A008969 A008970

tabf,nonn,nice,easy

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