a(n) = |b(n)|^2 = x^2 + 3*y^2 where (x,y,y,y) is the quaternion b(n) of the sequence b of quaternions defined by b(0)=1,b(1)=1, b(n) = b(n-1) + b(n-2)*(0,c,c,c) where c = 1/sqrt(3).

A105309

a(n) = |b(n)|^2 = x^2 + 3*y^2 where (x,y,y,y) is the quaternion b(n) of the sequence b of quaternions defined by b(0)=1,b(1)=1, b(n) = b(n-1) + b(n-2)*(0,c,c,c) where c = 1/sqrt(3).

Terms

    a(0) =1a(1) =1a(2) =2a(3) =5a(4) =9a(5) =20a(6) =41a(7) =85a(8) =178a(9) =369a(10) =769a(11) =1600a(12) =3329a(13) =6929a(14) =14418a(15) =30005a(16) =62441a(17) =129940a(18) =270409a(19) =562725a(20) =1171042a(21) =2436961a(22) =5071361a(23) =10553600a(24) =21962241a(25) =45703841a(26) =95110562a(27) =197926885a(28) =411889609a(29) =857150100

External references