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A009979 Powers of 35. 2
1, 35, 1225, 42875, 1500625, 52521875, 1838265625, 64339296875, 2251875390625, 78815638671875, 2758547353515625, 96549157373046875, 3379220508056640625, 118272717781982421875, 4139545122369384765625 (list; graph; refs; listen; history; internal format)
OFFSET

0,2

COMMENTS

If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4,5,6} such that for fixed y_1,y_2,...,y_n in {1,2,3,4,5,6} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), May 24 2007

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 35-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

LINKS

T. D. Noe, Table of n, a(n) for n=0..100

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Tanya Khovanova, Recursive Sequences

FORMULA

G.f.: 1/(1-35*x). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 24 2008]

a(n)=35^n; a(n)=35*a(n-1) n>0 a(0)=1 [From Vincenzo Librandi, Nov 21 2010]

MATHEMATICA

35^Range[0, 15] (* From Harvey P. Dale, Sep 10 2011 *)

PROG

(MAGMA)[35^n: n in [0..100]] [From Vincenzo Librandi, Nov 21 2010]

CROSSREFS

Sequence in context: A126158 A200724 A095153 * A158733 A029560 A195617

Adjacent sequences:  A009976 A009977 A009978 * A009980 A009981 A009982

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 13 13:51 EST 2012. Contains 205488 sequences.