OFFSET
1,2
COMMENTS
Numerators of fractions in partial sums of Sum_{n>=0} 11^n/1000^(n+1) converging to fraction 1/989 or Sum_{n>=0} 10^n/999^(n+1) whose alternating sum converges to fraction 1/1009 [= alternating sum_9^n/1000^(n+1)].
LINKS
Colin Barker, Table of n, a(n) for n = 1..334
Index entries for linear recurrences with constant coefficients, signature (1011,-11000).
FORMULA
From Colin Barker, Oct 02 2015: (Start)
a(n) = 1011*a(n-1) - 11000*a(n-2) for n>2.
G.f.: x / ((11*x-1)*(1000*x-1)).
(End)
EXAMPLE
As overlapping Pascal triangles starting a new triangle to the left of each row skipping one place:
....................1
...............1.0.1.1
..........1.0.1.1.1.2.1
.....1.0.1.1.1.2.2.3.3.1
1.0.1.1.1.2.2.3.4.5.6.4.1
PROG
(PARI) Vec(x/((11*x-1)*(1000*x-1)) + O(x^40)) \\ Colin Barker, Oct 02 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mark Dols, May 27 2010
EXTENSIONS
Definition adapted to offset by Georg Fischer, Jun 19 2021
STATUS
approved