login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A003947
Expansion of (1+x)/(1-4*x).
98
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
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
FORMULA
Binomial transform of A060925. Its binomial transform is A003463 (without leading zero). - Paul Barry, May 19 2003
From Paul Barry, May 19 2003: (Start)
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. (End)
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
(Magma) [1] cat [5*4^(n-1): n in [1..30]]; // G. C. Greubel, Aug 10 2019
(Sage) [1]+[5*4^(n-1) for n in (1..30)] # G. C. Greubel, Aug 10 2019
(GAP) Concatenation([1], List([1..30], n-> 5*4^(n-1) )); # G. C. Greubel, Aug 10 2019
CROSSREFS
Cf. A003948, A003949. Column 5 in A265583.
Sequence in context: A170590 A170638 A170686 * A369837 A363508 A252698
KEYWORD
nonn,easy,changed
EXTENSIONS
Edited by N. J. A. Sloane, Dec 04 2009
STATUS
approved