Traces of the matrices (A345197) counting integer compositions by length and alternating sum.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =3a(5) =3a(6) =6a(7) =15a(8) =24a(9) =43a(10) =92a(11) =171a(12) =315a(13) =629a(14) =1218a(15) =2313a(16) =4523a(17) =8835a(18) =17076a(19) =33299a(20) =65169a(21) =127065a(22) =248330a(23) =486669a(24) =953130a(25) =1867973a(26) =3666732a(27) =7200085a(28) =14144077a(29) =27810171