Number of Carlitz compositions of n (see A003242) such that the first and last parts are equal.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =3a(6) =2a(7) =7a(8) =11a(9) =17a(10) =26a(11) =54a(12) =86a(13) =155a(14) =272a(15) =464a(16) =816a(17) =1447a(18) =2507a(19) =4400a(20) =7706a(21) =13456a(22) =23570a(23) =41293a(24) =72212a(25) =126394a(26) =221282a(27) =387219a(28) =677714a(29) =1186311