A081202 8th binomial transform of (0,1,0,1,0,1,....), A000035.

0, 1, 16, 193, 2080, 21121, 206896, 1979713, 18640960, 173533441, 1602154576, 14701866433, 134294124640, 1222488408961, 11099284691056, 100571785292353, 909893629141120, 8222275592839681, 74233110849544336, 669726411243809473, 6038936596379658400, 54430221633714537601

Offset

0,3

Comments

Binomial transform of A081201.

From Wolfdieter Lang, Jul 17 2017: (Start)

For a combinatorial interpretation of a(n) with special 9-letter words of length n see the comment in A081200 on the 7-letter analog.

The binomial transform of {a(n)}_{n >=0} is A081203, the 10-letter analog.

(End)

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (16,-63).

Formula

a(n) = 16*a(n-1) - 63*a(n-2), a(0)=0, a(1)=1.

G.f.: x/((1-7*x)*(1-9*x)).

a(n) = (9^n - 7^n)/2.

E.g.f.: exp(7*x)*(exp(2*x) - 1)/2. - Stefano Spezia, Jul 23 2024

Mathematica

Join[{a=0, b=1}, Table[c=16*b-63*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
CoefficientList[Series[x / ((1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)

Prog

(Magma) [9^n/2 - 7^n/2: n in [0..25]]; // Vincenzo Librandi, Aug 07 2013

Crossrefs

Cf. A000035, A016178, A081200, A081201, A081203.

Sequence in context: A120994 A374070 A016178 * A196803 A292785 A081185

Adjacent sequences: A081199 A081200 A081201 * A081203 A081204 A081205

Keyword

easy,nonn

Author

Paul Barry, Mar 11 2003

Status

approved