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A141135
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Minimal number of unit edges required to construct n regular pentagons when allowing edge-sharing.
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0
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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
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OFFSET
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1,1
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LINKS
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Ralph H. Buchholz and Warwick de Launey, Edge minimization, June 1996, (revised June 2008).
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FORMULA
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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
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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Ralph H. Buchholz (teufel_pi(AT)yahoo.com), Jun 08 2008
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EXTENSIONS
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STATUS
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approved
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