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A237187
Total number of possible evolutions arising from n tandem duplications of DNA.
1
1, 11, 627, 154869, 156882297, 640550418651, 10485169802898219, 686977840316088410661, 180074066392854674644514625, 188817562686559733371879032616875, 791953915642546445046738160803339091875, 13286762105932889434920130050786333382153423125
OFFSET
1,2
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..57
L. Penso-Dolfin and C. D. Greenman, The Combinatorics of Tandem Duplication, arXiv:1402.0104v1 [math.CO], Feb 1, 2014.
FORMULA
a(n) = Product_{k=1..n} (4^k - (2*k+1)).
EXAMPLE
a(4) = (4^1 - (2*1+1)) * (4^2 - (2*2+1)) * (4^3 - (2*3+1)) * (4^4 - (2*4+1)).
MATHEMATICA
a[n_] := Product[4^k - 2 k - 1, {k, 1, n}]; Array[a, 12] (* Robert G. Wilson v, Feb 17 2014 *)
PROG
(PARI) a(n) = prod(k=1, n, 4^k - (2*k+1)); \\ Michel Marcus, Feb 04 2014
CROSSREFS
Sequence in context: A115737 A319835 A288549 * A201175 A211401 A036933
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Feb 04 2014
EXTENSIONS
More terms from Michel Marcus, Feb 04 2014
STATUS
approved