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A003947 Coordination sequence for infinite tree with valency 5. +0
4
1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520 (list; graph; listen)
OFFSET

0,2

COMMENT

For n>=1, a(n+1) is equal to the number of functions f:{1,2,...,n+1}->{1,2,3,4,5} such that for fixed, different x_1, x_2,...,x_n in {1,2,...,n+1} and fixed y_1, y_2,...,y_n in {1,2,3,4,5} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), May 10 2007

LINKS

T. D. Noe, Table of n, a(n) for n=0..200

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 306

Index entries for sequences related to trees

FORMULA

Binomial transform of A060925. Its binomial transform is A003463 (without leading zero). - Paul Barry (pbarry(AT)wit.ie), May 19 2003

a(n)=(5*4^n-0^n)/4; G.f.: (1+x)/(1-4x); E.g.f.: (5exp(4x)-exp(0))/4. - Paul Barry (pbarry(AT)wit.ie), May 19 2003

a(n) = Sum_{ 0<=k<=n } A029653(n, k)*x^k for x = 3 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 10 2005

MAPLE

k := 5; if n = 0 then 1 else k*(k-1)^(n-1); fi;

CROSSREFS

Sequence in context: A028814 A079820 A117422 this_sequence A033131 A022021 A030520

Adjacent sequences: A003944 A003945 A003946 this_sequence A003948 A003949 A003950

KEYWORD

nonn

AUTHOR

njas

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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