

A111284


Number of permutations of [n] avoiding the patterns {2143, 2341, 2413, 2431, 3142, 3241, 3412, 3421, 4123, 4213, 4231, 4321, 4132, 4312}; number of strong sorting classes based on 2143.


8



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
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OFFSET

1,2


COMMENTS

This sequence might also be called "The NonPythagorean integers" since no primitive Pythagorean triangle (PPT) exists containing them. Numbers of the form 4n2 cannot 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

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. 183185.
Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGrawHill Book Company, New York (1968).


LINKS

M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb. 12 (2005) R31


FORMULA

a(n) = 4*n6, n>=2.


MATHEMATICA



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



