OFFSET
0,1
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).
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 03 2012
STATUS
approved