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Search: id:A003947
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| A003947 |
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Coordination sequence for infinite tree with valency 5. |
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+0
4
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| 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)
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OFFSET
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0,2
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COMMENT
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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
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LINKS
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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
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FORMULA
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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
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MAPLE
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k := 5; if n = 0 then 1 else k*(k-1)^(n-1); fi;
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CROSSREFS
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Sequence in context: A028814 A079820 A117422 this_sequence A033131 A022021 A030520
Adjacent sequences: A003944 A003945 A003946 this_sequence A003948 A003949 A003950
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KEYWORD
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nonn
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AUTHOR
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njas
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