OFFSET
0,1
COMMENTS
Numerator of g.f. is on half of row polynomial Sum_{m=0..2} A061187(1,m) * x^m.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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
2*a(n) = A060924(n+1, 1).
G.f.: (1+x)*(3-2*x)/(1-3*x+x^2)^2.
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4), with a(0)=3, a(1)=19, a(2)=79, a(3)=283. - Harvey P. Dale, Oct 11 2012
a(n) = Fibonacci(2*n+4) + n*Lucas(2*n+3). - Lechoslaw Ratajczak, May 06 2020
MATHEMATICA
CoefficientList[Series[(1+x)(3-2x)/(1-3x+x^2)^2, {x, 0, 30}], x] (* or *) LinearRecurrence[{6, -11, 6, -1}, {3, 19, 79, 283}, 30] (* Harvey P. Dale, Oct 11 2012 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+x)*(3-2*x)/(1-3*x+x^2)^2) \\ G. C. Greubel, Dec 21 2017
(Magma) I:=[3, 19, 79, 283]; [n le 4 select I[n] else 6*Self(n-1) - 11*Self(n-2) + 6*Self(n-3) - Self(n-4): n in [1..30]]; // G. C. Greubel, Dec 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 20 2001
STATUS
approved