OFFSET
0,2
REFERENCES
Ralph P. Grimaldi, Fibonacci and Catalan Numbers: An Introduction, (2012). See Property 10.3 at pp. 56-58.
LINKS
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 210, formula page 204).
Index entries for linear recurrences with constant coefficients, signature (15,-25).
FORMULA
G.f.: -(5*x-1) / (25*x^2-15*x+1). - Colin Barker, Aug 29 2013
a(n) = 5^n*A001519(n+1). - R. J. Mathar, Jul 26 2019
From Stefano Spezia, Nov 16 2025: (Start)
a(n) = Sum_{k=0..2*n+1} binomial(2*n+1, k)*A000045(k)^2 (see Grimaldi).
E.g.f.: exp(15*x/2)*(5*cosh(5*sqrt(5)*x/2) + sqrt(5)*sinh(5*sqrt(5)*x/2))/5. (End)
MAPLE
A123358 := proc(n)
option remember;
if n <= 1 then
op(n+1, [1, 10]) ;
else
15*procname(n-1)-25*procname(n-2) ;
end if
end proc:
seq( A123358(n), n=0..30) ; # R. J. Mathar, Jul 26 2019
MATHEMATICA
LinearRecurrence[{15, -25}, {1, 10}, 30] (* Jean-François Alcover, Apr 03 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 10 2006
STATUS
approved