A319 Captain describes the procedural and clearance deviations that he suffered before declaring fatigue and removing himself from the pairing.

Narrative

Fatigue issue actually started during takeoff the flight before. As the pilot flying; I elected to use TOGA for takeoff; LLWS alert in effect but none reported. Crew set MCT/FLEX at takeoff after 80 KTS ECAM warning appeared throttle position. First Officer verified power setting was good and we continued. It wasn't until 1;200 with climb power selected that we both realize that TOGA was not set. In the departure briefing; I verified TOGA was to be used and requested that the power be set/checked by 80 KTS. The rest of the flight was normal; minimum radio traffic at XA00; until we started descent in to ZZZ. 2 radio calls were missed and one; during approach; required verification 3 times for heading and altitude change. Considered calling out fatigue in ZZZ; not wanting to cause a system delay; after a cup of coffee and aircraft preparation I felt that the ZZZ to ZZZ1 leg could be made safely. At pushback; missed the Before Start checklist call. After engine start; missed the taxi light; brake pressure check and taxi instructions. The First Officer was alert and said he was not fatigued and we continued. After takeoff; a few missed calls but no serious issue. Asked the First Officer to verify all settings and readbacks. Advised the company by ACARS that I would need to be replaced in ZZZ1 for the ZZZZ turn. This flight meets all FAR requirements; but is not safe by any standard. Scheduling is exposing the crew to 3 low operation performance periods; 2 of which are in 1 duty period. In NASA's testimony before Congress; they reported: 'The period 3-5 AM is a circadian low point for performance and alertness. During this time; the brain triggers sleep and sleepiness. The other period of increased sleepiness is roughly 3-5 PM. This continued shifting of work cycles; night/day; day/night and 4 legs duty period that start on the back side; 3-5 AM; continuing through the 3-5 PM period in the same duty period will result in an incident or accident.'