OFFSET
1,2
COMMENTS
(2*n, a(n)) are the solutions of Diophantine equation 3^x = 4*y + 5.
Second bisection of A080926. - Bruno Berselli, Feb 12 2013
Sum of n-th row of triangle of powers of 9: 1; 9 1 9; 81 9 1 9 81; 729 81 9 1 9 81 729; ... - Philippe Deléham, Feb 24 2014
REFERENCES
Jiri Herman, Radan Kucera and Jaromir Simsa, Equations and Inequalities, Springer (2000), p. 225 (5.3).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (10,-9).
FORMULA
G.f.: x*(1+9*x)/((1-x)*(1-9*x)). - Bruno Berselli, Feb 12 2013
a(n)-a(n-1) = A000792(6n-4). - Bruno Berselli, Feb 12 2013
a(n) = 9*a(n-1) + 10, a(1) = 1. - Philippe Deléham, Feb 24 2014
a(n) = -A084222(2*n). - Philippe Deléham, Feb 24 2014
EXAMPLE
a(1) = 1;
a(2) = 9 + 1 + 9 = 19;
a(3) = 81 + 9 + 1 + 9 + 81 = 181;
a(4) = 729 + 81 + 9 + 1 + 9 + 81 + 729 = 1639; etc. - Philippe Deléham, Feb 24 2014
MAPLE
MATHEMATICA
(9^Range[25] - 5)/4 (* Bruno Berselli, Feb 12 2013 *)
CoefficientList[Series[(1 + 9 x)/((1 - x) (1 - 9 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 26 2014 *)
PROG
(Haskell)
a211866 = (flip div 4) . (subtract 5) . (9 ^)
(Maxima) makelist((9^n-5)/4, n, 1, 30); /* Martin Ettl, Feb 12 2013 */
(Magma) I:=[1, 19]; [n le 2 select I[n] else 10*Self(n-1)-9*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Feb 26 2014
(PARI) a(n)=(9^n-5)/4 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Feb 12 2013
STATUS
approved