The most important syllabic nasal sound in English language is /n/. Syllabic /n/ is commonly found after alveolar plosives and fricatives, not very often found after non-alveolar consonants, after bilabial consonants, and after velar consonants.
A good example for this situation is the word "eaten". In the case of /t/ and /d/ if they are followed by the syllabic nasal /n/, the plosive is nasally released. In our example, the word "eaten" /ˈitn/, the soft plate is lowered at the end of /t/ so the air is released through the nose. One more observation should be made here. The syllabic nasal /n/ is not found after /l/, /tʃ/ or /dʒ/. So, the word "pigeon" /ˈpɪdʒən/ doesn’t have the syllabic /n/ after /dʒ/.
A good example for this situation is the word "happen" /ˈhæpən/. While many people, including me, pronounce it without a syllabic /n/ (but with /ən/), it is equally acceptable to pronounce it with a syllabic /n/, /ˈhæpn/. In a similar way, after velar consonants, syllabic /n/ and /ən/ are equally acceptable such as in the word "waken".
Let’s take a look at the word "wagon" /ˈwægən/. This is the usual pronunciation and we might say that in words where the syllable following a velar consonant is spelled "an" or "on" it is rarely heard. Pronunciation with /ən/ is far more common.