Number of filaments with n square cells.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =7a(6) =13a(7) =31a(8) =65a(9) =154a(10) =347a(11) =824a(12) =1905a(13) =4512a(14) =10546a(15) =24935a(16) =58476a(17) =138002a(18) =323894a(19) =763172a(20) =1790585a(21) =4213061a(22) =9878541a(23) =23214728a(24) =54393063a(25) =127687369a(26) =298969219a(27) =701171557a(28) =1640683309a(29) =3844724417