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URL: https://oeis.org/A187709

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A187709
a(n) = (7*9^n + 1)/8.
7
1, 8, 71, 638, 5741, 51668, 465011, 4185098, 37665881, 338992928, 3050936351, 27458427158, 247125844421, 2224132599788, 20017193398091, 180154740582818, 1621392665245361, 14592533987208248, 131332805884874231, 1181995252963868078, 10637957276674812701, 95741615490073314308, 861674539410659828771
OFFSET
0,2
COMMENTS
Case r=9 in a(n)=((r-2)*r^n+1)/(r-1).
FORMULA
a(n) = (7*9^n + 1)/8.
a(n) = +10*a(n-1) -9*a(n-2).
a(n) = 8*Sum_{i=0..n-1} a(i) -n + 1.
G.f.: (1-2*x)/((1-x)*(1-9*x)).
a(n) = 9^n - Sum_{i=0..n-1} 9^i for n>0. - Bruno Berselli, Jun 20 2013
E.g.f.: (7*exp(9*x) + exp(x))/8. - G. C. Greubel, Nov 06 2018
MATHEMATICA
(7*9^Range[0, 30]+1)/8 (* or *) LinearRecurrence[{10, -9}, {1, 8}, 30] (* Harvey P. Dale, Jul 20 2012 *)
PROG
(Magma) [(7*9^n+1)/8: n in [0..25]]; // Vincenzo Librandi, Mar 30 2011
(PARI) a(n)=(7*9^n+1)/8 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Cf. A007051, A083068, A270472 (first differences), A059482: cases r=3,8,10 in ((r-2)*r^n+1)/(r-1), respectively.
Sequence in context: A015576 A070998 A370178 * A292865 A152265 A081178
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Mar 30 2011
EXTENSIONS
Additional formulas from Bruno Berselli
STATUS
approved