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 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. 10
 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 (list; graph; refs; listen; history; text; internal format)
 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 non-congruent 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 Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe) 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: k-gon partitions, Bull. Austral Math. Soc., 64 (2001), 321-329. Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 1, -1, 0, 0, -1, 1, -1, 1, 1, -1). FORMULA G.f.: x^4*(1+x+x^5)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)). a(2*n+6) = A026810(2*n+6) - A000601(n), a(2*n+7) = A026810(2*n+7) - A000601(n) for n >= 0. - Seiichi Manyama, Jun 08 2017 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. MATHEMATICA CoefficientList[Series[x^4*(1+x+x^5)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)), {x, 0, 60}], x] (* Frank M Jackson, Jun 09 2017 *) CROSSREFS Number of k-gons that can be formed with perimeter n: A005044 (k=3), this sequence (k=4), A069906 (k=5), A069907 (k=6), A288253 (k=7), A288254 (k=8), A288255 (k=9), A288256 (k=10). 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

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)