OFFSET
3,2
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (1111,-112110,1111000,-1000000)
FORMULA
O.g.f.: x^3/((1 - x)*(1 - 10*x)*(1 - 100*x)*(1 - 1000*x)).
E.g.f.: (-1000 + 1110*exp(9*x) - 111*exp(99*x) + exp(999*x))*exp(x)/890109000.
a(n) = 1111*a(n-1) - 112110*a(n-2) + 1111000*a(n-3) - 1000000*a(n-4).
a(n) = ((10^n - 100)*(10^n - 10)*(10^n - 1))/890109000.
a(n) = Product_{i=0..2} (1 - 10^(n-i))/(1 - 10^(i+1)).
MATHEMATICA
Table[((10^n - 100) (10^n - 10) (10^n - 1))/890109000, {n, 0, 15}]
Table[QBinomial[n, 3, 10], {n, 3, 15}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Aug 13 2016
STATUS
approved