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

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

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

Index entries for sequences related to dominoes

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

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

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