A203570 Bisection of A201207 (half-convolution of the Lucas sequence A000032 with itself); even part.

4, 7, 27, 84, 270, 826, 2488, 7353, 21461, 61960, 177344, 503892, 1422892, 3996619, 11173935, 31114236, 86328978, 238764238, 658478176, 1811322045, 4970928809, 13613135152, 37208048132, 101518052904, 276527670100, 752102592271

Offset

0,1

Comments

The odd part of the bisection of A201207 is given in A203574.

See a comment on A201204 for the definition of the half-convolution of a sequence with itself, and the rule for the o.g.f.s of the bisection. Here the o.g.f. is (Lconve(x) + L2(x))/2, with the o.g.f. Lconve(x) = (4-11*x+11*x^2+x^3)/

(1-3*x+x^2)^2 of A203573 and the o.g.f. L2(x)= (4-7*x-x^2)/ ((1+x)*(1-3*x+x^2)) of A001254. This leads to the o.g.f. given in the formula section.

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = A201207(2*n), n>=0.

a(n) = (2*(4*n+6)*F(2*n+1)-4*(n+1)*F(2*n))/4 + (-1)^n, with the Fibonacci numbers F(n)=A000045(n).

O.g.f.: (4-13*x+4*x^3+12*x^2)/((1-3*x+x^2)^2*(1+x)). See a comment above.

Crossrefs

Cf. A201207, A203574.

Sequence in context: A303844 A197789 A076148 * A146085 A359067 A061668

Adjacent sequences: A203567 A203568 A203569 * A203571 A203572 A203573

Keyword

nonn

Author

Wolfdieter Lang, Jan 03 2012

Status

approved