|
| |
|
|
A047220
|
|
Numbers that are congruent to {0, 1, 3} mod 5.
|
|
24
|
|
|
|
0, 1, 3, 5, 6, 8, 10, 11, 13, 15, 16, 18, 20, 21, 23, 25, 26, 28, 30, 31, 33, 35, 36, 38, 40, 41, 43, 45, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, 66, 68, 70, 71, 73, 75, 76, 78, 80, 81, 83, 85, 86, 88, 90, 91, 93, 95, 96, 98, 100, 101, 103, 105, 106
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
First differences are (1,2,2), repeat, with period 3 (A130196). - N. J. A. Sloane, Dec 03 2015
Also numbers k such that k*(k+2)*(k+4) is divisible by 5. - Bruno Berselli, Dec 28 2017
Maximum sum of degeneracies over all decompositions of the complete graph of order n into four factors. The extremal decompositions are characterized in the Bickle link below. - Allan Bickle, Dec 21 2021
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Allan Bickle, Nordhaus-Gaddum Theorems for k-Decompositions, Congr. Num. 211 (2012) 171-183.
Z. Furedi, A. Kostochka, M. Stiebitz, R. Skrekovski, and D. West, Nordhaus-Gaddum-type theorems for decompositions into many parts, J. Graph Theory 50 (2005), 273-292.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
|
|
|
FORMULA
|
a(n) = floor(5*(n-1)/3). - Gary Detlefs, Feb 20 2010
a(n) = 2*n - floor(n/3) - (n^2 mod 3), with offset 0. - Gary Detlefs, Mar 19 2010
G.f.: x^2*(1 + 2*x + 2*x^2)/(1 - x)^2/(1 + x + x^2). - Colin Barker, Feb 17 2012
a(n) = n + floor(2*(n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 5*n/3 - 2 + 2*sin(2*n*Pi/3)/(3*sqrt(3)).
a(3*k) = 5*k-2, a(3*k-1) = 5*k-4, a(3*k-2) = 5*k-5. (End)
E.g.f.: 2 + (5*x - 6)*exp(x)/3 + 2*sin(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2))/(3*sqrt(3)). - Ilya Gutkovskiy, Jun 14 2016
|
|
|
MAPLE
|
seq(floor(5*(n-1)/3), n=1..56); # Gary Detlefs, Feb 20 2010
seq(2*n-floor(n/3)-(n^2 mod 3), n=0..55); # Gary Detlefs, Mar 19 2010
|
|
|
MATHEMATICA
|
Table[Floor[5*(n-1)/3], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)
|
|
|
PROG
|
(Magma) I:=[0, 1, 3, 5]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // Vincenzo Librandi, Apr 26 2012
(PARI) a(n)=n + 2*(n-1)\3 - 1 \\ Charles R Greathouse IV, Sep 24 2015
|
|
|
CROSSREFS
|
Cf. A011655, A130196 (first differences).
Sequence in context: A247913 A188046 A244644 * A329845 A329993 A064994
Adjacent sequences: A047217 A047218 A047219 * A047221 A047222 A047223
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
