OFFSET
0,3
COMMENTS
Numerators of fractions in partial sums of sum_{n=0...infinity} 101^n/1000^(n+1)converging to fraction 1/899 or sum_{n=0...infinity} 100^n/999^(n+1) whose alternating sum converges to fraction 1/1099 [= alternating sum_99^n/1000^(n+1)].
LINKS
Colin Barker, Table of n, a(n) for n = 0..334
Index entries for linear recurrences with constant coefficients, signature (1101,-101000).
FORMULA
From Colin Barker, Oct 02 2015: (Start)
a(n) = 1101*a(n-1) - 101000*a(n-2) for n>2.
G.f.: x / ((101*x-1)*(1000*x-1)).
(End)
EXAMPLE
As interlocking Pascal triangles starting a new triangle to the left of each row:
................1
............1.1.0.1
........1.1.1.1.2.0.1
....1.1.1.2.2.3.1.3.0.1
1.1.1.2.3.3.5.3.6.1.4.0.1
MATHEMATICA
RecurrenceTable[{a[0]==0, a[n]==1000*a[n-1]+101^(n-1)}, a, {n, 15}] (* Harvey P. Dale, Nov 18 2013 *)
PROG
(PARI) concat(0, Vec(x/((101*x-1)*(1000*x-1)) + O(x^30))) \\ Colin Barker, Oct 02 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mark Dols, May 27 2010
EXTENSIONS
Prepended zero (from definition), changed offset accordingly, and more terms from Harvey P. Dale, Nov 18 2013
STATUS
approved