OFFSET
0,2
COMMENTS
In general, sum{k=0..floor(n/2), C(2n-2k,2k)a^k*b^(n-k)} has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).
LINKS
Index entries for linear recurrences with constant coefficients, signature (20,-80,200,-100).
FORMULA
G.f.: (1-10x-10x^2)/(1-20x-80x^2-200x^3+100x^4); a(n)=20a(n-1)+80a(n-2)+200a(n-3)-100a(n-4).
MATHEMATICA
Table[Sum[Binomial[2n-2k, 2k]10^(n-k), {k, 0, Floor[n/2]}], {n, 0, 30}] (* or *) LinearRecurrence[{20, -80, 200, -100}, {1, 10, 110, 1600}, 30] (* Harvey P. Dale, Mar 20 2023 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 04 2005
STATUS
approved