OFFSET
1,4
REFERENCES
S. J. Cyvin, B. N. Cyvin, and J. Brunvoll. Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), 55-70, Table 1 Symmetry C_s.
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,0,-30,25).
FORMULA
From R. J. Mathar, Jul 31 2019: (Start)
G.f.: -4*x^4/((x - 1)*(5*x - 1)*(5*x^2 - 1)).
4*a(n) = 5^(n-2) + 1 - 10*A056487(n-4). (End)
E.g.f.: (25*cosh(x) + cosh(5*x) - 10*cosh(sqrt(5)*x) + 25*sinh(x) + sinh(5*x) - 6*sqrt(5)*sinh(sqrt(5)*x) - 16)/100. - Stefano Spezia, Jun 06 2023
MAPLE
A121102 := proc(n)
local mr, ar, cr, dr , ir, p5;
if n = 1 then
ar := 1 ;
else
ar := 0 ;
end if;
dr := 1-ar ;
p5 := 5^(floor(n/2)-1) ;
if n = 1 then
cr :=0 ;
else
cr := (p5-1)/2+2*ar/5 ;
end if;
mr := (3-2*(-1)^n)*p5/2-1/2 ;
if n = 1 then
ir := 1;
else
ir := (5^(n-2)+1)/4 +(2-(-1)^n)*p5/2 -3*ar/5 ;
end if;
ir-ar-dr-cr-mr ;
end proc:
seq(A121102(n), n=1..30) ; # R. J. Mathar, Jul 31 2019
MATHEMATICA
LinearRecurrence[{6, 0, -30, 25}, {0, 0, 0, 4}, 27] (* Jean-François Alcover, Mar 31 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 11 2006
STATUS
approved