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A178396
a(1)=1, a(n) = a(n-1)*1000 + 11^(n-1) for n>=2.
1
1, 1011, 1011121, 1011122331, 1011122345641, 1011122345802051, 1011122345803822561, 1011122345803842048171, 1011122345803842262529881, 1011122345803842264887828691, 1011122345803842264913766115601, 1011122345803842264914051427271611
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)].
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
Sequence in context: A185881 A115769 A267613 * A178349 A291962 A094946
KEYWORD
nonn,easy
AUTHOR
Mark Dols, May 27 2010
EXTENSIONS
Definition adapted to offset by Georg Fischer, Jun 19 2021
STATUS
approved