Number of subsets of {1,...,n} containing a subset of the form {k,k+1,k+3} for some k.

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =2a(5) =7a(6) =19a(7) =46a(8) =107a(9) =242a(10) =535a(11) =1162a(12) =2490a(13) =5281a(14) =11108a(15) =23206a(16) =48206a(17) =99663a(18) =205218a(19) =421115a(20) =861585a(21) =1758249a(22) =3580075a(23) =7275377a(24) =14759592a(25) =29897683a(26) =60481359a(27) =122206014a(28) =246665382a(29) =497414751