a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A026659.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =14a(5) =21a(6) =55a(7) =98a(8) =255a(9) =421a(10) =1047a(11) =1939a(12) =4851a(13) =8393a(14) =20265a(15) =38423a(16) =93728a(17) =166999a(18) =395317a(19) =761724a(20) =1824934a(21) =3319575a(22) =7745123a(23) =15103234a(24) =35691596a(25) =65946113a(26) =152151529a(27) =299476048a(28) =700050056a(29) =1309537115