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A155666
a(n) = 9^n - 8^n + 1.
9
1, 2, 18, 218, 2466, 26282, 269298, 2685818, 26269506, 253202762, 2413042578, 22791125018, 213710059746, 1992110014442, 18478745943858, 170706760005818, 1571545212141186, 14425381885981322, 132080236787517138, 1206736529597136218, 11004743954450081826, 100195617094657583402
OFFSET
0,2
FORMULA
G.f.: 1/(1-9*x)-1/(1-8*x)+1/(1-x).
E.g.f.: exp(9*x)-exp(8*x)+exp(x).
a(n) = 17*a(n-1)-72*a(n-2)+56 with a(0) = 1, a(1) = 2. - Vincenzo Librandi, Jul 21 2010
MATHEMATICA
Table[9^n-8^n+1, {n, 0, 20}] (* or *) LinearRecurrence[{18, -89, 72}, {1, 2, 18}, 20] (* Harvey P. Dale, Aug 16 2015 *)
PROG
(PARI) a(n)=9^n-8^n+1 \\ Charles R Greathouse IV, Jun 11 2015
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Jan 31 2009
STATUS
approved