

A062890


Number of quadrilaterals that can be formed with perimeter n. In other words, number of partitions of n into four parts such that the sum of any three is more than the fourth.


6



0, 0, 0, 0, 1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 12, 16, 18, 23, 24, 31, 33, 41, 43, 53, 55, 67, 69, 83, 86, 102, 104, 123, 126, 147, 150, 174, 177, 204, 207, 237, 241, 274, 277, 314, 318, 358, 362, 406, 410, 458, 462, 514, 519, 575, 579, 640, 645, 710
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OFFSET

0,8


COMMENTS

Partition sets of n into four parts (sides) such that the sum of any three is more than the fourth do not uniquely define a quadrilateral, even if it is further constrained to be cyclic. This is because the order of adjacent sides is important. E.g. the partition set [1,1,2,2] for a perimeter n=6 can be reordered to generate two noncongruent cyclic quadrilaterals, [1,2,1,2] and [1,1,2,2], where the first is a rectangle and the second a kite.  Frank M Jackson, Jun 29 2012


LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000
G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package, p. 19.
G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis IX: kgon partitions, Bull. Austral Math. Soc., 64 (2001), 321329.


FORMULA

G.f.: x^4*(1+x+x^5)/((1x^2)*(1x^3)*(1x^4)*(1x^6)).


EXAMPLE

a(7) = 2 as the two partitions are (1,2,2,2), (1,1,2,3) and in each sum of any three is more than the fourth.


CROSSREFS

Cf. A005044, A069906, A069907.
Sequence in context: A166159 A169693 A180121 * A259626 A058586 A090467
Adjacent sequences: A062887 A062888 A062889 * A062891 A062892 A062893


KEYWORD

nonn,easy


AUTHOR

Amarnath Murthy, Jun 29 2001


EXTENSIONS

More terms from Vladeta Jovovic and Dean Hickerson, Jul 01 2001


STATUS

approved



