OFFSET
1,1
LINKS
C. Kimberling, Problem 10520, Amer. Math. Mon. 103 (1996) p. 347.
Index entries for linear recurrences with constant coefficients, signature (2,1,-3,0,1).
FORMULA
a(n) = (1/4)*(8*Lucas(n+1) - 2n - 5 + (-1)^n), n > 1.
G.f.: x*(x^5 + x^4 - 4*x^2 + 3)/((1 - x)*(1 - x^2)*(1 - x - x^2)).
E.g.f.: (4*exp(x/2)*(cosh(sqrt(5)*x/2) + sqrt(5)*sinh(sqrt(5)*x/2)) - (2 + x)*cosh(x) - (3 + x)*sinh(x) - 2*(1 + x))/2. - Stefano Spezia, Feb 24 2023
MATHEMATICA
CoefficientList[Series[x (x^5+x^4-4x^2+3)/((1-x)(1-x^2)(1-x-x^2)), {x, 0, 30}], x] (* Harvey P. Dale, May 10 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, May 10 2018
a(29)-a(32) corrected and more terms from Sean A. Irvine, May 05 2019
Name edited by Michel Marcus, Jul 06 2019
STATUS
approved