A247842 a(n) = Sum_{k=2..n} 9^k.
0, 81, 810, 7371, 66420, 597861, 5380830, 48427551, 435848040, 3922632441, 35303692050, 317733228531, 2859599056860, 25736391511821, 231627523606470, 2084647712458311, 18761829412124880, 168856464709124001, 1519708182382116090, 13677373641439044891
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (10,-9).
Programs
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Magma
[0] cat [&+[9^k: k in [2..n]]: n in [2..30]];
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Magma
[(9^(n+1)-81)/8: n in [1..30]];
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Maple
A247842:=n->add(9^k, k=2..n): seq(A247842(n), n=1..30); # Wesley Ivan Hurt, Sep 26 2014
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Mathematica
RecurrenceTable[{a[1] == 0, a[n] == a[n-1] + 9^n}, a, {n, 30}] (* or *) CoefficientList[Series[81 x / ((1 - x) (1 - 9 x)), {x, 0, 30}], x]
Formula
G.f.: 81*x^2/((1-x)*(1-9*x)).
a(n) = a(n-1) + 9^n = (9^(n+1) - 81)/8 = 10*a(n-1) - 9*a(n-2).
a(n) = A052386(n) - 9. - Michel Marcus, Sep 25 2014