Consider 3 X 3 matrix M = [0 1 0 / 0 0 1 / 5 2 0]; a(n) = the center term in M^n * [1 1 1].

Terms

a(0) =1a(1) =7a(2) =7a(3) =19a(4) =49a(5) =73a(6) =193a(7) =391a(8) =751a(9) =1747a(10) =3457a(11) =7249a(12) =15649a(13) =31783a(14) =67543a(15) =141811a(16) =294001a(17) =621337a(18) =1297057a(19) =2712679a(20) =5700799a(21) =11910643a(22) =24964993a(23) =52325281a(24) =109483201a(25) =229475527a(26) =480592807a(27) =1006367059a(28) =2108563249a(29) =4415698153