Number of 3-colored integer partitions such that no adjacent parts have the same color.

Terms

a(0) =1a(1) =3a(2) =9a(3) =21a(4) =51a(5) =111a(6) =249a(7) =525a(8) =1119a(9) =2319a(10) =4809a(11) =9825a(12) =20079a(13) =40671a(14) =82341a(15) =165945a(16) =334191a(17) =671307a(18) =1347861a(19) =2702385a(20) =5416395a(21) =10847787a(22) =21720981a(23) =43474869a(24) =87004875a(25) =174081051a(26) =348279777a(27) =696712749a(28) =1393674603a(29) =2787673767