OFFSET
0,2
COMMENTS
Binomial transform is A099912.
LINKS
Eric Weisstein's World of Mathematics, Herschel Graph.
Index entries for linear recurrences with constant coefficients, signature (10,1,-10).
FORMULA
G.f.: (1-7*x-6*x^2)/((1-x^2)*(1-10*x)).
a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3).
a(n) = (-1)^n/11 + 8*10^n/33 + 2/3.
E.g.f.: exp(-x) * (8*exp(11*x) + 22*exp(2*x) + 3)/33. - Amiram Eldar, Jan 11 2026
MATHEMATICA
LinearRecurrence[{10, 1, -10}, {1, 3, 25}, 20] (* Amiram Eldar, Jan 11 2026 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 30 2004
STATUS
approved