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

Author

Wolfdieter Lang, Jan 03 2012

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Crossrefs

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

Programs

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 *)

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