A081035 8th binomial transform of the periodic sequence (1,9,1,1,9,1...).
1, 17, 209, 2273, 23201, 228017, 2186609, 20620673, 192174401, 1775688017, 16304021009, 148995991073, 1356782533601, 12321773100017, 111671069983409, 1010465414433473, 9132169221980801, 82455386442384017, 743959522093353809, 6708663007623467873, 60469158230094196001
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (16,-63).
Programs
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Magma
[5*9^n-4*7^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
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Mathematica
CoefficientList[Series[(1 + x)/((1 - 7 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *) LinearRecurrence[{16,-63},{1,17},30] (* Harvey P. Dale, Oct 07 2014 *) -
PARI
a(n)=5*9^n-4*7^n \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = 9*a(n-1) + 8*7^(n-1).
a(n) = 5*9^n - 4*7^n.
G.f.: (1+x)/((1-7*x)*(1-9*x)). - Vincenzo Librandi, Aug 06 2013
a(0)=1, a(1)=17, a(n)=16*a(n-1)-63*a(n-2). - Harvey P. Dale, Oct 07 2014
E.g.f.: exp(7*x)*(5*exp(2*x) - 4). - Stefano Spezia, Jul 23 2024