T(n,k)=Number of length n 1..(k+1) arrays with every leading partial sum divisible by 2, 3, 5 or 7.

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =6a(5) =4a(6) =4a(7) =12a(8) =18a(9) =8a(10) =5a(11) =20a(12) =45a(13) =50a(14) =16a(15) =6a(16) =28a(17) =80a(18) =130a(19) =105a(20) =27a(21) =7a(22) =36a(23) =125a(24) =264a(25) =331a(26) =181a(27) =33a(28) =8a(29) =46