login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047264 Numbers that are congruent to 0 or 5 mod 6. 8
0, 5, 6, 11, 12, 17, 18, 23, 24, 29, 30, 35, 36, 41, 42, 47, 48, 53, 54, 59, 60, 65, 66, 71, 72, 77, 78, 83, 84, 89, 90, 95, 96, 101, 102, 107, 108, 113, 114, 119, 120, 125, 126, 131, 132, 137, 138, 143, 144, 149 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Values of n for which Sum_{k=1..n} k*Fibonacci(k) is even (n > 0). Example: 5 is in the sequence because Sum_{k=1..5} k*Fibonacci(k) = 1*1 + 2*1 + 3*2 + 4*3 + 5*5 = 46. - Emeric Deutsch, Mar 28 2005

For a(n) is the n-th Tower of Hanoi move, the smallest disc (#1) is on peg A.  If n == (1,2) mod 6, the disc is on peg C; and if n == (3,4) mod 6, the disc is on peg B. Disc #1 rotates C,B,A,C,B,A,C,B,A,... All discs start at "0" on peg A. Disc #1 is on peg A again for moves (5,6), (11,12), (17,18), ... - Gary W. Adamson, Jun 23 2012

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

H. Freitag, Problem B-776: An Even Sum, Fibonacci Quarterly, 32 (1994), no. 5, ibid. 34 (1996), no. 1, p. 85.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = 3*n + (-1)^n - 2.

a(n) = 6*n - a(n-1) - 7 (with a(1)=0). - Vincenzo Librandi, Aug 05 2010

G.f.: x^2*(5+x) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

Let b(1)=0, b(2)=1 and b(k+2) = b(k+1) - b(k) + k^2; then a(n) is the sequence of integers such that b(a(n)) is a square = (a(n) + 1)^2. - Benoit Cloitre, Sep 04 2002

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=5 and b(k)=A007283(k) for k > 0. - Philippe Deléham, Oct 17 2011

EXAMPLE

From Vincenzo Librandi, Aug 05 2010: (Start)

a(2) = 6*2 - 0 - 7 = 5;

a(3) = 6*3 - 5 - 7 = 6;

a(4) = 6*4 - 6 - 7 = 11. (End)

MAPLE

c:=proc(n) if n mod 6 = 0 or n mod 6 = 5 then n else fi end: seq(c(n), n=0..149); # Emeric Deutsch, Mar 28 2005

MATHEMATICA

Select[Range[0, 149], MemberQ[{0, 5}, Mod[#, 6]] &] (* or *)

Fold[Append[#1, 6 #2 - Last@ #1 - 7] &, {0}, Range[2, 50]] (* or *)

Rest@ CoefficientList[Series[x^2*(5 + x)/((1 + x) (x - 1)^2), {x, 0, 50}], x] (* Michael De Vlieger, Jan 12 2018 *)

PROG

(PARI) forstep(n=0, 200, [5, 1], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

CROSSREFS

Complement of A047227.

Sequence in context: A046608 A228357 A215033 * A277095 A190895 A129286

Adjacent sequences:  A047261 A047262 A047263 * A047265 A047266 A047267

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 06:12 EST 2019. Contains 320389 sequences. (Running on oeis4.)