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A003947
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G.f.: (1+x)/(1-4*x).
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59
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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, 87960930222080, 351843720888320
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Coordination sequence for infinite tree with valency 5.
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
| T. D. Noe, Table of n, a(n) for n = 0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 306
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index to divisibility sequences
Index to sequences with linear recurrences with constant coefficients, signature (4).
Index entries for sequences related to trees
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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
a(n)=A146523(n)*A011782(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 08 2009]
a(n)=5*4^(n-1) (with a(0)=1), also a(n)=4*a(n-1), n>1; a(0)=1, a(1)=5. [From Vincenzo Librandi, Dec 31 2010]
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MAPLE
| k := 5; if n = 0 then 1 else k*(k-1)^(n-1); fi;
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MATHEMATICA
| q = 5; Join[{a = 1}, Table[If[n != 0, a = q*a - a, a = q*a], {n, 0, 25}]] (* and *) Join[{1}, 5*4^Range[0, 25]] (* From Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
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PROG
| (PARI) a(n)=5*4^n\4 \\ Charles R Greathouse IV, Sep 08 2011
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CROSSREFS
| Cf. A003948, A003949.
Sequence in context: A170590 A170638 A170686 * A033131 A022021 A165203
Adjacent sequences: A003944 A003945 A003946 * A003948 A003949 A003950
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2009.
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