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 A141135 Minimal number of unit edges required to construct n regular pentagons when allowing edge-sharing. 0
 5, 9, 13, 17, 21, 24, 28, 32, 36, 39, 43, 47, 50, 54, 58, 61, 65, 69, 72, 76, 80, 83, 87, 90, 94, 98, 101, 105, 109, 112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..30. Ralph H. Buchholz, Spiral polygon series, preprint 1985 SMJ 31, School Mathematics Journal, 1995. Ralph H. Buchholz and Warwick de Launey, Edge minimization, June 1996, (revised June 2008). Ralph H. Buchholz and Warwick de Launey, An edge minimization problem for regular polygons, The Electronic Journal of Combinatorics, Volume 16, Issue 1 (2009), #R90. FORMULA Conjectures from Colin Barker, Apr 05 2019: (Start) G.f.: x*(5 + 4*x + 4*x^2 - x^3 - x^5 + x^8 - x^9) / ((1 - x)^2*(1 + x + x^2)). a(n) = a(n-1) + a(n-3) - a(n-4) for n>10. (End) Conjecture: if n is a term in A121149, a(n) = a(n-1) + 3, otherwise a(n) = a(n-1) + 4. - Jinyuan Wang, Apr 05 2019 EXAMPLE a(6) = 24 since the first pentagon requires 5 edges, the 2nd, 3rd, 4th and 5th pentagons require an additional 4 edges each and the 6th pentagon requires 3 edges since it can share 2 edges (if one tiles via a 6-cycle). Thus 24 = 5 + 4 + 4 + 4 + 4 + 3. CROSSREFS Cf. equilateral triangles A137228, squares A078633, regular hexagons A135708. Cf. A121149. Sequence in context: A314666 A314667 A086408 * A363379 A194395 A162502 Adjacent sequences: A141132 A141133 A141134 * A141136 A141137 A141138 KEYWORD nonn,more AUTHOR Ralph H. Buchholz (teufel_pi(AT)yahoo.com), Jun 08 2008 EXTENSIONS a(21)-a(30) from Jinyuan Wang, Apr 05 2019 STATUS approved

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Last modified March 4 22:06 EST 2024. Contains 370532 sequences. (Running on oeis4.)