Length of lists created by n substitutions k -> Range[0,Mod[k+1,4]] starting with {0}.

Terms

a(0) =1a(1) =2a(2) =5a(3) =14a(4) =38a(5) =102a(6) =273a(7) =731a(8) =1958a(9) =5245a(10) =14050a(11) =37636a(12) =100816a(13) =270057a(14) =723405a(15) =1937794a(16) =5190793a(17) =13904642a(18) =37246538a(19) =99772766a(20) =267262553a(21) =715919535a(22) =1917742590a(23) =5137081001a(24) =13760762966a(25) =36861127432a(26) =98740361920a(27) =264497039329