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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, 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)
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 11 2003
STATUS
approved