A203573 Bisection of A099924 (convolution of Lucas numbers); even arguments.

4, 13, 45, 152, 491, 1531, 4652, 13865, 40713, 118144, 339559, 968183, 2742100, 7721797, 21637221, 60367976, 167787107, 464776435, 1283571068, 3535240289, 9713031489, 26627195728, 72847698655, 198929987567, 542305383076, 1476061431421

Offset

0,1

Comments

One half of the odd part of the bisection of A099924 is found in A203574.

Links

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

É. Czabarka, R. Flórez, L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.

Index entries for linear recurrences with constant coefficients, signature (6, -11, 6, -1).

Formula

a(n) = A099924(2*n), n>=0.

O.g.f.: (4-11*x+11*x^2+x^3)/(1-3*x+x^2)^2.

a(n) = 4*(n+1)*F(2*n+1)-(2*n+1)*F(2*n), n>=0, with the Fibonacci numbers F(n)=A000045(n). From the partial fraction decomposition of the o.g.f. and the Fibonacci recurrence.

a(0)=4, a(1)=13, a(2)=45, a(3)=152, a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3)-a(n-4). - Harvey P. Dale, Jan 11 2014

Mathematica

CoefficientList[Series[(4-11x+11x^2+x^3)/(1-3x+x^2)^2, {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -11, 6, -1}, {4, 13, 45, 152}, 30] (* Harvey P. Dale, Jan 11 2014 *)

Crossrefs

Cf. A000032, A000045, A099924, 2*A203574.

Sequence in context: A192255 A035356 A320652 * A214997 A189348 A165205

Adjacent sequences: A203570 A203571 A203572 * A203574 A203575 A203576

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 03 2012

Status

approved