a(n) = Sum_{i=0..n} Sum_{j=0..n} 2^max(i,j).

Terms

a(0) =1a(1) =7a(2) =27a(3) =83a(4) =227a(5) =579a(6) =1411a(7) =3331a(8) =7683a(9) =17411a(10) =38915a(11) =86019a(12) =188419a(13) =409603a(14) =884739a(15) =1900547a(16) =4063235a(17) =8650755a(18) =18350083a(19) =38797315a(20) =81788931a(21) =171966467a(22) =360710147a(23) =754974723a(24) =1577058307a(25) =3288334339a(26) =6845104131a(27) =14227079171a(28) =29527900163a(29) =61203283971