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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
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
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.)