|
| |
| |
|
|
|
1, 1, 4, 2, 7, 3, 10, 4, 13, 5, 16, 6, 19, 7, 22, 8, 25, 9, 28, 10, 31, 11, 34, 12, 37, 13, 40, 14, 43, 15, 46, 16, 49, 17, 52, 18, 55, 19, 58, 20, 61, 21, 64, 22, 67, 23, 70, 24, 73, 25, 76, 26, 79, 27, 82, 28, 85, 29, 88, 30, 91, 31, 94, 32, 97, 33, 100, 34, 103, 35, 106, 36
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| a(n) is a diagonal of Table A123685.
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,2,0,-1)
|
|
|
FORMULA
| G.f.: x*(1+x+2*x^2)/((1-x)^2*(1+x)^2); a(n) = n - 1/4 - (1/2*n - 1/4)*(-1)^n; a(2n-1) = A016777(n-1) = 3(n-1)+1, a(2n) = A000027(n) = n; a(n) = A071045(n-1)+1; a(n) = A093005(n) - A093005(n-1) for n > 1; a(n) = A105638(n+2) - A105638(n+1) for n > 1; a(n) = A092530(n) - A092530(n-1)-1; a(n) = A031878(n+1) - A031878(n)-1. - Klaus Brockhaus, May 12 2007
a(1+2*n)+a(2+2*n) = 2+4*n = A016825(n). Paul Curtz , Mar 09 2011.
a(n)= +2*a(n-2) -a(n-4). Paul Curtz , Mar O9 2011.
Contribution from Jaroslav Krizek, Mar 22 2011 (Start):
a(n) = n + a(n-1) for odd n. a(n) = n - A064455(n-1) for even n.
a(n) = A064455(n) - A137501(n).
Abs(a(n) - A064455(n)) = A052928(n). (End)
|
|
|
EXAMPLE
| The natural numbers begin 1,2,3,...A000027
Seq 3*n + 1 begins 1,4,7,10, ... A016777
so A123684 begins
1,1,4,2,7,3,10,...
|
|
|
PROG
| (MAGMA) &cat[ [ 3*n-2, n ]: n in [1..36] ]; /* Klaus Brockhaus, May 12 2007 */
(PARI) 1. print(vector(72, n, if(n%2==0, n/2, (3*n-1)/2))); 2. print(vector(72, n, n-1/4-(1/2*n-1/4)*(-1)^n)); /* Klaus Brockhaus, May 12 2007 */
|
|
|
CROSSREFS
| Cf. A000027, A016777, A123685, A071045, A093005, A105638, A092530, A031878.
Sequence in context: A126091 A026189 A026213 * A180076 A169756 A002949
Adjacent sequences: A123681 A123682 A123683 * A123685 A123686 A123687
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Oct 11 2006
|
|
|
EXTENSIONS
| More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 12 2007
|
| |
|
|
