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A003947 Expansion of (1+x)/(1-4*x). 63
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; text; internal format)
OFFSET

0,2

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 Janjic, May 10 2007

Number of length-n strings of 5 letters with no two adjacent letters identical. The general case (strings of r letters) is the sequence with g.f. (1+x)/(1-(r-1)*x). [Joerg Arndt, Oct 11 2012]

Create a rectangular prism with edges of lengths 2^(n-2), 2^(n-1), and 2^(n) starting at n=2; then the surface area = a(n). - J. M. Bergot, Aug 08 2013

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 entries for linear recurrences with constant coefficients, signature (4).

Index entries for sequences related to trees

FORMULA

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

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

a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 3 . - Philippe Deléham, Jul 10 2005

a(n) = A146523(n)*A011782(n). [R. J. Mathar, Jul 08 2009]

a(n) = 5*A000302(n-1), n>0.

a(n) = 4*a(n-1), n>1. [Vincenzo Librandi, Dec 31 2010]

G.f.: 2+x- 2/G(0), where G(k)= 1 + 1/(1 - x*(5*k-4)/(x*(5*k+1) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 04 2013

MAPLE

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

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]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)

LinearRecurrence[{4}, {1, 5}, 30] (* Harvey P. Dale, Apr 19 2015 *)

PROG

(PARI) a(n)=5*4^n\4 \\ Charles R Greathouse IV, Sep 08 2011

CROSSREFS

Cf. A003948, A003949. Column 5 in A265583.

Sequence in context: A170590 A170638 A170686 * A252698 A271196 A033131

Adjacent sequences:  A003944 A003945 A003946 * A003948 A003949 A003950

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by N. J. A. Sloane, Dec 04 2009

STATUS

approved

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Last modified March 27 12:35 EDT 2017. Contains 284176 sequences.