A081036 9th binomial transform of the periodic sequence (1,10,1,1,10,1...).
1, 19, 262, 3196, 36568, 402544, 4320352, 45562816, 474502528, 4896020224, 50168161792, 511345294336, 5190762354688, 52526098837504, 530208790700032, 5341670325600256, 53733362604802048, 539866900838416384, 5418935206707331072, 54351481653658648576, 544811853229269188608
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (18,-80).
Programs
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Magma
[(11/2)*10^n-(9/2)*8^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013
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Mathematica
CoefficientList[Series[(1 + x)/((1 - 8 x) (1 - 10 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *) LinearRecurrence[{18,-80},{1,19},20] (* Harvey P. Dale, Aug 16 2014 *)
Formula
a(n) = 10*a(n-1) + 9*8^(n-1).
a(n) = (11/2)*10^n - (9/2)*8^n.
G.f.: (1+x)/((1-8*x)*(1-10*x)). - Vincenzo Librandi, Aug 06 2013
a(0)=1, a(1)=19, a(n)=18*a(n-1)-80*a(n-2). - Harvey P. Dale, Aug 16 2014
E.g.f.: exp(8*x)*(11*exp(2*x) - 9)/2. - Stefano Spezia, Jul 23 2024
Extensions
Corrected by T. D. Noe, Nov 07 2006