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A203570 Bisection of A201207 (half-convolution of the Lucas sequence A000032 with itself); even part. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A061668 A239025

Adjacent sequences:  A203567 A203568 A203569 * A203571 A203572 A203573

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Jan 03 2012

STATUS

approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)