|
| |
|
|
A111284
|
|
Number of permutations avoiding the patterns {2143,2341,2413,2431,3142,3241,3412,3421,4123,4213,4231,4321,4132,4312}; number of strong sorting class based on 2143.
|
|
3
| |
|
|
1, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| This sequence might also be called "The Non-Pythagorean integers" since no primitive Pythagorean triangle (PPT) exists containing them. Numbers of form 2n+2 (where n is even) can not be a leg or hypotenuse of PPT [a,b,c]. This excludes all even members of the present sequence. Integers 1 and zero are excluded because they form a 'degenerate triangle' with angles = 0. Compare A125667. - H. Lee Price, Feb 02 2007
Besides the first term this sequence is the denominator of (pi/8)=(1/2)-(1/6)+(1/10)-(1/14)+(1/18)-(1/22)+.... - Mohammad K. Azarian, Oct 14 2011
|
|
|
REFERENCES
| M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb. 12 (2005)
Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
Granino A. Korn and Theresa M.Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968).
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
|
|
|
FORMULA
| a(n) = 4*n-6, n>=2.
a(n) = A016825(n-2), n>1. [From R. J. Mathar, Aug 18 2008]
G.f.: x(1+3x^2)/(1-x)^2. [From R. J. Mathar, Nov 10 2008]
|
|
|
MATHEMATICA
| Table[If[n == 1, 1, 4n - 6], {n, 60}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 04 2005)
|
|
|
CROSSREFS
| Cf. A125667.
Sequence in context: A187884 A068977 * A130824 A016825 A161718 A122905
Adjacent sequences: A111281 A111282 A111283 * A111285 A111286 A111287
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Len Smiley ( smiley (at) math.uaa.alaska.edu ), Nov 01 2005
|
|
|
EXTENSIONS
| More terms from Robert G. Wilson v, Nov 04 2005
|
| |
|
|
