s(n+3)/4, where s is A024959.

Terms

a(0) =1a(1) =2a(2) =5a(3) =12a(4) =28a(5) =66a(6) =172a(7) =440a(8) =1108a(9) =2784a(10) =7552a(11) =20040a(12) =52336a(13) =136896a(14) =374688a(15) =1013056a(16) =2710016a(17) =7243104a(18) =20078784a(19) =55031040a(20) =149414144a(21) =405759232a(22) =1130565632a(23) =3125798656a(24) =8582582272a(25) =23543099392a(26) =66051398144a(27) =183922571264a(28) =508945206272