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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (18,-80).

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

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 *)

Prog

(Magma) [(11/2)*10^n-(9/2)*8^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

Crossrefs

Cf. A081034, A081035.

Sequence in context: A017917 A016308 A014923 * A244652 A142817 A294828

Adjacent sequences: A081033 A081034 A081035 * A081037 A081038 A081039

Keyword

nonn,easy

Author

Paul Barry, Mar 03 2003

Extensions

Corrected by T. D. Noe, Nov 07 2006

Status

approved