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A081202 8th binomial transform of (0,1,0,1,0,1,....), A000035. 8
0, 1, 16, 193, 2080, 21121, 206896, 1979713, 18640960, 173533441, 1602154576, 14701866433, 134294124640, 1222488408961, 11099284691056, 100571785292353, 909893629141120, 8222275592839681, 74233110849544336, 669726411243809473 (list; graph; refs; listen; history; text; internal format)
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) = 16a(n-1)-63a(n-2), a(0)=0, a(1)=1.

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

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

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: A218176 A120994 A016178 * A196803 A292785 A081185

Adjacent sequences:  A081199 A081200 A081201 * A081203 A081204 A081205

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)