combinations without specified separations

We consider the restricted subsets of $mathbb{n}_n={1,2,ldots,n}$ with $qgeq1$ being the largest member of the set $mathcal{q}$ of disallowed differences between subset elements. we obtain new results on various classes of problem involving such combinations lacking specified separations.  in particular, we find recursion relations for the number of $k$-subsets for any $mathcal{q}$ when $|{mathbb{n}_q-mathcal{q}}|leq2$.  the results are obtained, in a quick and intuitive manner, as a consequence of a bijection we give between such subsets and the restricted-overlap tilings of an $(n+q)$-board (a linear array of $n+q$ square cells of unit width) with squares ($1times1$ tiles) and combs.  a $(w_1,g_1,w_2,g_2,ldots,g_{t-1},w_t)$-comb is composed of $t$ sub-tiles known as teeth.  the $i$-th tooth in the comb has width $w_i$ and is separated from the $(i+1)$-th tooth by a gap of width $g_i$. here we only consider combs with $w_i,g_iinmathbb{z}^+$.  when performing a restricted-overlap tiling of a board with such combs and squares, the leftmost cell of a tile must be placed in an empty cell whereas the remaining cells in the tile are permitted to overlap other non-leftmost filled cells of tiles already on the board.