Kenyon Martin’s plan when he joined the Knicks three weeks ago was simple. After his first day of practice with the team, Martin explained what he wanted when he humbly became the first No. 1 overall N.B.A. pick in league history to sign a 10-day contract. “Another 10 days,” he said before adding, “and then the rest of the season.” Martin accomplished his objective Friday as the Knicks signed him for the remainder of the season after his second 10-day contract expired. During his 20 days, Martin averaged 5.7 points and 3.2 rebounds in six games played. Coach Mike Woodson is likely to rely on Martin more during the last month of the season. He has become even more important since the Knicks’ frontcourt is full of star players battling knee injuries.