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We construct a set $H$ of orthogonal polynomial sequences that contains allthe families in the Askey scheme and the $q$-Askey scheme. The polynomialsequences in $H$ are solutions of a generalized first-order difference equationwhich is determined by three linearly recurrent sequences of numbers. Two ofthese sequences are solutions of a difference equation of order three and theother sequence satisfies a related difference equation of order five.  We obtain explicit expressions for the coefficients of the orthogonalpolynomials and for the generalized moments with respect to a basis of Newtontype of the space of polynomials. We also obtain explicit formulas for thecoefficients of the three-term recurrence relation satisfied by the polynomialsequences in $H$.  The set $H$ contains all the 15 families in the Askey scheme and all the 29families in the $q$-Askey scheme. Each of these families is obtained by directsubstitution of appropriate values for the parameters in our general formulas.The only cases that require some limits are the Hermite and continuous$q$-Hermite polynomials. We present the values of the parameters for some ofthe families.

A unified construction of all the hypergeometric and basic hypergeometric families of orthogonal polynomial sequences