0,1

A106729 is sum of two consecutive squares of Lucas numbers (A001254), for which L(n)^2 + L(n+1)^2 = 5*{F(n)^2 + F(n+1)^2} = 5*A001519(n). Axxxxxx is sum of two consecutive squares of Lucas 3-step numbers (A001644). Sum of two consecutive squares of Lucas 4-step numbers can be expressed in terms of tetranacci numbers, but not quite as neatly.

a(n) = A073817(n)^2 + A073817(n+1)^2. a(n) = 5*A073817(n)^2 + 4*A073817(n)*A073817(n-4) + A073817(n-4)^2.

a(0) = A073817(0)^2 + A073817(1)^2 = 4^2 + 1^2 = 16 + 1 = 17.

a(1) = A073817(1)^2 + A073817(2)^2 = 1^2 + 3^2 = 1 + 9 = 10.

a(2) = A073817(2)^2 + A073817(3)^2 = 3^2 + 7^2 = 9 + 49 = 58.

a(3) = A073817(3)^2 + A073817(4)^2 = 7^2 + 15^2 = 49 + 225 = 274.

a(4) = A073817(4)^2 + A073817(5)^2 = 15^2 + 26^2 = 225 + 676 = 901 = 30^2 + 1.

a(5) = A073817(5)^2 + A073817(6)^2 = 26^2 + 51^2 = 676 + 2601 = 3277.

Cf. A073817, A106729.

Sequence in context: A113779 A061049 A166524 this_sequence A040274 A164064 A073887

Adjacent sequences: A106788 A106789 A106790 this_sequence A106792 A106793 A106794

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), May 16 2005