A081203 9th binomial transform of (0,1,0,1,0,1,.....), A000035.

0, 1, 18, 244, 2952, 33616, 368928, 3951424, 41611392, 432891136, 4463129088, 45705032704, 465640261632, 4725122093056, 47800976744448, 482407813955584, 4859262511644672, 48874100093157376, 490992800745259008

Offset: 0

Author

Paul Barry, Mar 11 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081202.

From Wolfdieter Lang, Jul 17 2017: (Start)

For a combinatorial interpretation of a(n) with special 10-letter words of length n see the comment in A081200 on the 7-letter analog.

The binomial transform of {a(n)}_{n >= 0} is {0, A016190}, the 11-letter analog.

(End)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (18,-80).

Crossrefs

Apart from the first term, identical to A016186.

Cf. A000035, A016190, A081202, A081200, A081201, A081202.

Programs

Magma

[10^n/2 - 8^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

Mathematica

CoefficientList[Series[x / ((1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{18,-80},{0,1},20] (* Harvey P. Dale, Aug 05 2018 *)

Formula

a(n) = 18*a(n-1)-80*a(n-2), a(0)=0, a(1)=1.

G.f.: x/((1-8*x)*(1-10*x)).

a(n) = 10^n/2 - 8^n/2.